## Output from calis32.sas

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```                  TEST32: Vocabulary Test Data, LORD (1957)                  1
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

FACTOR Model Statement
-------------------------------
Matrix         Rows & Cols          Matrix Type```
``` TERM   1-----------------------------------------------------------
1    _F_            4       2    GENERAL
2    _P_            2       2    SYMMETRIC
TERM   2-----------------------------------------------------------
3    _U_            4       4    SYMMETRIC

```
```                      Initial Parameter Matrix _P_[2:2]
Symmetric Matrix
Constant Model Matrix```
```                                    FCOR1       FCOR2

FCOR1        1.00        1.00
FCOR2        1.00        1.00
```
```                      Initial Parameter Matrix _F_[4:2]
Lower Triangular Matrix```
```                                   FACT1           FACT2

X1         .  [Z1]          .0
X2         .  [Z1]          .0
Y1          .0             .  [Z3]
Y2          .0             .  [Z3]
```
```                      Initial Parameter Matrix _U_[4:4]
Diagonal Matrix```
```                 UVAR1             UVAR2             UVAR3             UVAR4

X1         .  [EPS1]          .0                .0                .0
X2          .0               .  [EPS1]          .0                .0
Y1          .0                .0               .  [EPS3]          .0
Y2          .0                .0                .0               .  [EPS3]```

```                  TEST32: Vocabulary Test Data, LORD (1957)                  2
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          2
4 Variables          Model Matrices       3
10 Informations       Parameters           4

VARIABLE              Mean           Std Dev

X1                       0       9.295047068
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942
```
```
Covariances
```
```                    X1                X2                Y1                Y2

X1       86.39790000       57.77510000       56.86510000       58.89860000
X2       57.77510000       86.26320000       59.31770000       59.66830000
Y1       56.86510000       59.31770000       97.28500000       73.82010000
Y2       58.89860000       59.66830000       73.82010000       97.81920000
Determinant = 7377416 (Ln = 15.814)

Some initial estimates computed by McDonald's method.

```
```                         Vector of Initial Estimates
```
```          Z1            1    8.48839  Matrix Entry: _F_[1:1] _F_[2:1]
Z3            2    9.25668  Matrix Entry: _F_[3:2] _F_[4:2]
EPS1          3   14.27773  Matrix Entry: _U_[1:1] _U_[2:2]
EPS3          4   11.86602  Matrix Entry: _U_[3:3] _U_[4:4]

```
```
Predetermined Elements of the Predicted Moment Matrix
```
```                    X1                X2                Y1                Y2

X1                 .                 .                 .                 .
X2                 .                 .                 .                 .
Y1                 .                 .                 .                 .
Y2                 .                 .                 .                 .
Sum of Squared Differences = 0```

```                  TEST32: Vocabulary Test Data, LORD (1957)                  3
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 4
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 1.541
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    2   0    0.2988   1.2425  0.0374   1.338   0.646
2    0    4   0    0.0580   0.2409 0.00451       0   0.796
3    0    5   0    0.0576 0.000314  0.0005       0   1.201
4    0    6   0    0.0576 0.000021 0.00015       0   1.308
5    0    7   0    0.0576 1.943E-6 0.00004       0   1.306
6    0    8   0    0.0576 1.819E-7 0.00001       0   1.306
7    0    9   0    0.0576 1.698E-8 4.15E-6       0   1.306

Optimization Results: Iterations= 7 Function Calls= 10 Jacobian Calls= 8
Active Constraints= 0  Criterion= 0.057613719
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                  4
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.33055005       51.64193499       60.66599376       60.66599376
X2       51.64193499       86.33055005       60.66599376       60.66599376
Y1       60.66599376       60.66599376       97.55210003       71.26694226
Y2       60.66599376       60.66599376       71.26694226       97.55210003
Determinant = 7814939 (Ln = 15.872)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                  5
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0576
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9705
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9509
Root Mean Square Residual (RMR) . . . . . . . . .     2.5430
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.9705
Chi-square = 37.3337       df = 6       Prob>chi**2 = 0.0001
Null Model Chi-square:     df = 6                  1466.5524
RMSEA Estimate  . . . . . .  0.0898  90%C.I.[0.0635, 0.1184]
Probability of Close Fit  . . . . . . . . . . . .     0.0076
ECVI Estimate . . . . . . .  0.0701  90%C.I.[0.0458, 0.1059]
Bentler's Comparative Fit Index . . . . . . . . .     0.9785
Normal Theory Reweighted LS Chi-square  . . . . .    39.3380
Akaike's Information Criterion. . . . . . . . . .    25.3337
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .    -7.5189
Schwarz's Bayesian Criterion. . . . . . . . . . .    -1.5189
McDonald's (1989) Centrality. . . . . . . . . . .     0.9761
Bentler & Bonett's (1980) Non-normed Index. . . .     0.9785
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9745
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.9745
Z-Test of Wilson & Hilferty (1931). . . . . . . .     4.5535
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9745
Bollen (1988) Non-normed Index Delta2 . . . . . .     0.9785
Hoelter's (1983) Critical N . . . . . . . . . . .        220

```
```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.067349946       6.133165014      -3.800893761      -1.767393761
X2       6.133165014      -0.067350054      -1.348293761      -0.997693761
Y1      -3.800893761      -1.348293761      -0.267100033       2.553157735
Y2      -1.767393761      -0.997693761       2.553157735       0.267099967
Average Absolute Residual = 1.727
Average Off-diagonal Absolute Residual = 2.767
```
```                      Rank Order of 5 Largest Residuals
```
```                   X2,X1     Y1,X1     Y2,Y1     Y2,X1     Y1,X2
6.1332   -3.8009    2.5532   -1.7674   -1.3483

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                  6
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Asymptotically Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.024781925       6.122637633      -1.873792731      -0.871302854
X2       6.122637633      -0.024781964      -0.664691835      -0.491850453
Y1      -1.873792731      -0.664691835      -0.102069370       6.125900219
Y2      -0.871302854      -0.491850453       6.125900219       0.102069345
Average Standardized Residual = 1.64
Average Off-diagonal Standardized Residual = 2.692
```
```        Rank Order of 5 Largest Asymptotically Standardized Residuals
```
```                   Y2,Y1     X2,X1     Y1,X1     Y2,X1     Y1,X2
6.1259    6.1226   -1.8738   -0.8713   -0.6647

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                  7
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Distribution of Asymptotically Standardized Residuals
(Each * represents 1 residuals)
```
```                     -2.00000 -   -1.75000  1  10.00% | *
-1.75000 -   -1.50000  0   0.00% |
-1.50000 -   -1.25000  0   0.00% |
-1.25000 -   -1.00000  0   0.00% |
-1.00000 -   -0.75000  1  10.00% | *
-0.75000 -   -0.50000  1  10.00% | *
-0.50000 -   -0.25000  1  10.00% | *
-0.25000 -          0  2  20.00% | **
0 -    0.25000  2  20.00% | **
0.25000 -    0.50000  0   0.00% |
0.50000 -    0.75000  0   0.00% |
0.75000 -    1.00000  0   0.00% |
1.00000 -    1.25000  0   0.00% |
1.25000 -    1.50000  0   0.00% |
1.50000 -    1.75000  0   0.00% |
1.75000 -    2.00000  0   0.00% |
2.00000 -    2.25000  0   0.00% |
2.25000 -    2.50000  0   0.00% |
2.50000 -    2.75000  0   0.00% |
2.75000 -    3.00000  0   0.00% |
3.00000 -    3.25000  0   0.00% |
3.25000 -    3.50000  0   0.00% |
3.50000 -    3.75000  0   0.00% |
3.75000 -    4.00000  0   0.00% |
4.00000 -    4.25000  0   0.00% |
4.25000 -    4.50000  0   0.00% |
4.50000 -    4.75000  0   0.00% |
4.75000 -    5.00000  0   0.00% |
5.00000 -    5.25000  0   0.00% |
5.25000 -    5.50000  0   0.00% |
5.50000 -    5.75000  0   0.00% |
5.75000 -    6.00000  0   0.00% |
6.00000 -    6.25000  2  20.00% | **

```
```                     Estimated Parameter Matrix _P_[2:2]
Symmetric Matrix
Constant Model Matrix```
```                     *** Constant or Unchanged Matrix ***

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                  8
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix _F_[4:2]
Standard Errors and t Values
Lower Triangular Matrix```
```                                   FACT1                  FACT2

X1        7.1862     [Z1]        0.
0.2660  27.0180        0.       0.

X2        7.1862     [Z1]        0.
0.2660  27.0180        0.       0.

Y1        0.                     8.4420     [Z3]
0.       0.            0.2800  30.1494

Y2        0.                     8.4420     [Z3]
0.       0.            0.2800  30.1494
```
```                     Estimated Parameter Matrix _U_[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                   UVAR1                   UVAR2

X1        34.6886   [EPS1]         0.
1.6463  21.0701         0.       0.

X2         0.                     34.6886   [EPS1]
0.       0.             1.6463  21.0701

Y1         0.                      0.
0.       0.             0.       0.

Y2         0.                      0.
0.       0.             0.       0.```

```                  TEST32: Vocabulary Test Data, LORD (1957)                  9
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix _U_[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                   UVAR3                   UVAR4

X1         0.                      0.
0.       0.             0.       0.

X2         0.                      0.
0.       0.             0.       0.

Y1        26.2852   [EPS3]         0.
1.3995  18.7812         0.       0.

Y2         0.                     26.2852   [EPS3]
0.       0.             1.3995  18.7812```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 10
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

```
```                                   FACT1             FACT2

X1      0.7734264128      0.0000000000
X2      0.7734264128      0.0000000000
Y1      0.0000000000      0.8547237097
Y2      0.0000000000      0.8547237097
```
```                        Squared Multiple Correlations
-------------------------------------------------------------
Error           Total
Parameter        Variance        Variance        R-squared
-------------------------------------------------------------```
```           1    X1          34.688615       86.330550        0.598188
2    X2          34.688615       86.330550        0.598188
3    Y1          26.285158       97.552100        0.730553
4    Y2          26.285158       97.552100        0.730553

```
```                    Correlations among Exogenous Variables
------------------------------------------------------
Row & Column          Parameter             Estimate
------------------------------------------------------```
```               2       1    FCOR2    FCOR1                1.000000

```
```
Factor Score Regression Coefficients
```
```                                   FACT1             FACT2

X1      0.0031342894      0.0031342894
X2      0.0031342894      0.0031342894
Y1      0.0028103118      0.0028103118
Y2      0.0028103118      0.0028103118
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 11
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices _P_[2:2]
Symmetric Matrix
Constant Model Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                    FCOR1                FCOR2

FCOR1        37.499               37.501
0.000  0.220         0.000 -0.110

FCOR2        37.501               37.504
0.000 -0.110         0.000  0.220
```
```             Rank order of 3 largest Lagrange multipliers in _P_
```
```              FCOR2 : FCOR2       FCOR2 : FCOR1       FCOR1 : FCOR1
37.5036 : 0.000     37.5015 : 0.000     37.4993 : 0.000

```
```              Lagrange Multiplier and Wald Test Indices _F_[4:2]
Lower Triangular Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                   FACT1                 FACT2

X1        729.974   [Z1]          0.120
0.729 -0.120

X2        729.974   [Z1]          0.120
0.729  0.120

Y1          0.069               908.987   [Z3]
0.793 -0.079

Y2          0.069               908.987   [Z3]
0.792  0.079```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 12
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Rank order of 4 largest Lagrange multipliers in _F_
```
```                 X1 : FACT2          X2 : FACT2          Y2 : FACT1
0.1201 : 0.729      0.1198 : 0.729      0.0692 : 0.792

Y1 : FACT1
0.0690 : 0.793

```
```              Lagrange Multiplier and Wald Test Indices _U_[4:4]
Diagonal Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                UVAR1              UVAR2              UVAR3              UVAR4

X1    443.949  [EPS1]     37.493             11.326              2.914
0.000  11.352      0.001  -5.150      0.088  -2.612

X2     37.493            443.949  [EPS1]      2.827              3.435
0.000  11.352                         0.093  -2.573      0.064  -2.836

Y1     11.326              2.827            352.733  [EPS3]     37.515
0.001  -5.150      0.093  -2.573                         0.000  15.666

Y2      2.914              3.435             37.515            352.733  [EPS3]
0.088  -2.612      0.064  -2.836      0.000  15.666
```
```             Rank order of 6 largest Lagrange multipliers in _U_
```
```                 Y2 : UVAR3          X2 : UVAR1          Y1 : UVAR1
37.5151 : 0.000     37.4930 : 0.000     11.3257 : 0.001

Y2 : UVAR2          Y2 : UVAR1          Y1 : UVAR2
3.4353 : 0.064      2.9138 : 0.088      2.8273 : 0.093

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 13
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Univariate Lagrange Multiplier Test
For Releasing Equality Constraints
-------------------------------------------------------------
Chi-Square    Prob          Change       Parameter  Equal to
-------------------------------------------------------------```
```            0.119951   0.7291  -0.0602 =   0.0597  _F_[1:1]= _F_[2:1]
0.069132   0.7926  -0.0396 =   0.0397  _F_[3:2]= _F_[4:2]
0.552416   0.4573   1.2260 =  -1.2246  _U_[1:1]= _U_[2:2]
0.242176   0.6226   0.7802 =  -0.7821  _U_[3:3]= _U_[4:4]

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 14
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

COSAN Model Statement
-------------------------------
Matrix         Rows & Cols          Matrix Type```
``` TERM   1-----------------------------------------------------------
1    F              4       2    GENERAL
2    PHI            2       2    SYMMETRIC
TERM   2-----------------------------------------------------------
3    U              4       4    DIAGONAL

```
```                      Initial Parameter Matrix PHI[2:2]
Symmetric Matrix
Constant Model Matrix```
```                                     COL1        COL2

ROW1        1.00        1.00
ROW2        1.00        1.00
```
```                       Initial Parameter Matrix F[4:2]
Lower Triangular Matrix```
```                                    COL1            COL2

X1         .  [Z1]          .0
X2         .  [Z1]          .0
Y1          .0             .  [Z3]
Y2          .0             .  [Z3]
```
```                       Initial Parameter Matrix U[4:4]
Diagonal Matrix```
```                  COL1              COL2              COL3              COL4

X1         .  [EPS1]          .0                .0                .0
X2          .0               .  [EPS1]          .0                .0
Y1          .0                .0               .  [EPS3]          .0
Y2          .0                .0                .0               .  [EPS3]```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 15
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          2
4 Variables          Model Matrices       3
10 Informations       Parameters           4

VARIABLE              Mean           Std Dev

X1                       0       9.295047068
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942
```
```
Covariances
```
```                    X1                X2                Y1                Y2

X1       86.39790000       57.77510000       56.86510000       58.89860000
X2       57.77510000       86.26320000       59.31770000       59.66830000
Y1       56.86510000       59.31770000       97.28500000       73.82010000
Y2       58.89860000       59.66830000       73.82010000       97.81920000
Determinant = 7377416 (Ln = 15.814)

```
```                         Vector of Initial Estimates
```
```          Z1            1    0.50000  Matrix Entry: F[1:1] F[2:1]
Z3            2    0.50000  Matrix Entry: F[3:2] F[4:2]
EPS1          3   50.00000  Matrix Entry: U[1:1] U[2:2]
EPS3          4   50.00000  Matrix Entry: U[3:3] U[4:4]

```
```
Predetermined Elements of the Predicted Moment Matrix
```
```                    X1                X2                Y1                Y2

X1                 .                 .                 .                 .
X2                 .                 .                 .                 .
Y1                 .                 .                 .                 .
Y2                 .                 .                 .                 .
Sum of Squared Differences = 0```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 16
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 4
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 3.101
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    2   0    1.0340   2.0674  0.0494   3.713   0.455
2    0    4   0    0.1144   0.9196  0.0288       0   1.660
3    0    5   0    0.0584   0.0560 0.00583       0   1.246
4    0    6   0    0.0576 0.000744 0.00054       0   1.086
5    0    7   0    0.0576 0.000019 0.00014       0   1.307
6    0    8   0    0.0576 1.774E-6 0.00004       0   1.306
7    0    9   0    0.0576  1.66E-7 0.00001       0   1.306
8    0   10   0    0.0576  1.55E-8 3.97E-6       0   1.306

Optimization Results: Iterations= 8 Function Calls= 11 Jacobian Calls= 9
Active Constraints= 0  Criterion= 0.057613719
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                 17
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.33055005       51.64186952       60.66598097       60.66598097
X2       51.64186952       86.33055005       60.66598097       60.66598097
Y1       60.66598097       60.66598097       97.55210003       71.26700254
Y2       60.66598097       60.66598097       71.26700254       97.55210003
Determinant = 7814939 (Ln = 15.872)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 18
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0576
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9705
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9509
Root Mean Square Residual (RMR) . . . . . . . . .     2.5430
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.9705
Chi-square = 37.3337       df = 6       Prob>chi**2 = 0.0001
Null Model Chi-square:     df = 6                  1466.5524
RMSEA Estimate  . . . . . .  0.0898  90%C.I.[0.0635, 0.1184]
Probability of Close Fit  . . . . . . . . . . . .     0.0076
ECVI Estimate . . . . . . .  0.0701  90%C.I.[0.0458, 0.1059]
Bentler's Comparative Fit Index . . . . . . . . .     0.9785
Normal Theory Reweighted LS Chi-square  . . . . .    39.3380
Akaike's Information Criterion. . . . . . . . . .    25.3337
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .    -7.5189
Schwarz's Bayesian Criterion. . . . . . . . . . .    -1.5189
McDonald's (1989) Centrality. . . . . . . . . . .     0.9761
Bentler & Bonett's (1980) Non-normed Index. . . .     0.9785
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9745
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.9745
Z-Test of Wilson & Hilferty (1931). . . . . . . .     4.5535
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9745
Bollen (1988) Non-normed Index Delta2 . . . . . .     0.9785
Hoelter's (1983) Critical N . . . . . . . . . . .        220

```
```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.067349951       6.133230476      -3.800880966      -1.767380966
X2       6.133230476      -0.067350049      -1.348280966      -0.997680966
Y1      -3.800880966      -1.348280966      -0.267100030       2.553097459
Y2      -1.767380966      -0.997680966       2.553097459       0.267099970
Average Absolute Residual = 1.727
Average Off-diagonal Absolute Residual = 2.767
```
```                      Rank Order of 5 Largest Residuals
```
```                   X2,X1     Y1,X1     Y2,Y1     Y2,X1     Y1,X2
6.1332   -3.8009    2.5531   -1.7674   -1.3483

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 19
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Asymptotically Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.024781909       6.122679434      -1.873786249      -0.871296466
X2       6.122679434      -0.024781945      -0.664685466      -0.491844099
Y1      -1.873786249      -0.664685466      -0.102069468       6.125796197
Y2      -0.871296466      -0.491844099       6.125796197       0.102069445
Average Standardized Residual = 1.64
Average Off-diagonal Standardized Residual = 2.692
```
```        Rank Order of 5 Largest Asymptotically Standardized Residuals
```
```                   Y2,Y1     X2,X1     Y1,X1     Y2,X1     Y1,X2
6.1258    6.1227   -1.8738   -0.8713   -0.6647

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 20
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Distribution of Asymptotically Standardized Residuals
(Each * represents 1 residuals)
```
```                     -2.00000 -   -1.75000  1  10.00% | *
-1.75000 -   -1.50000  0   0.00% |
-1.50000 -   -1.25000  0   0.00% |
-1.25000 -   -1.00000  0   0.00% |
-1.00000 -   -0.75000  1  10.00% | *
-0.75000 -   -0.50000  1  10.00% | *
-0.50000 -   -0.25000  1  10.00% | *
-0.25000 -          0  2  20.00% | **
0 -    0.25000  2  20.00% | **
0.25000 -    0.50000  0   0.00% |
0.50000 -    0.75000  0   0.00% |
0.75000 -    1.00000  0   0.00% |
1.00000 -    1.25000  0   0.00% |
1.25000 -    1.50000  0   0.00% |
1.50000 -    1.75000  0   0.00% |
1.75000 -    2.00000  0   0.00% |
2.00000 -    2.25000  0   0.00% |
2.25000 -    2.50000  0   0.00% |
2.50000 -    2.75000  0   0.00% |
2.75000 -    3.00000  0   0.00% |
3.00000 -    3.25000  0   0.00% |
3.25000 -    3.50000  0   0.00% |
3.50000 -    3.75000  0   0.00% |
3.75000 -    4.00000  0   0.00% |
4.00000 -    4.25000  0   0.00% |
4.25000 -    4.50000  0   0.00% |
4.50000 -    4.75000  0   0.00% |
4.75000 -    5.00000  0   0.00% |
5.00000 -    5.25000  0   0.00% |
5.25000 -    5.50000  0   0.00% |
5.50000 -    5.75000  0   0.00% |
5.75000 -    6.00000  0   0.00% |
6.00000 -    6.25000  2  20.00% | **

```
```                     Estimated Parameter Matrix PHI[2:2]
Symmetric Matrix
Constant Model Matrix```
```                     *** Constant or Unchanged Matrix ***

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 21
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix F[4:2]
Standard Errors and t Values
Lower Triangular Matrix```
```                                    COL1                   COL2

X1        7.1862     [Z1]        0.
0.2660  27.0180        0.       0.

X2        7.1862     [Z1]        0.
0.2660  27.0180        0.       0.

Y1        0.                     8.4420     [Z3]
0.       0.            0.2800  30.1494

Y2        0.                     8.4420     [Z3]
0.       0.            0.2800  30.1494
```
```                      Estimated Parameter Matrix U[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                    COL1                    COL2

X1        34.6887   [EPS1]         0.
1.6463  21.0701         0.       0.

X2         0.                     34.6887   [EPS1]
0.       0.             1.6463  21.0701

Y1         0.                      0.
0.       0.             0.       0.

Y2         0.                      0.
0.       0.             0.       0.```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 22
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix U[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                    COL3                    COL4

X1         0.                      0.
0.       0.             0.       0.

X2         0.                      0.
0.       0.             0.       0.

Y1        26.2851   [EPS3]         0.
1.3995  18.7812         0.       0.

Y2         0.                     26.2851   [EPS3]
0.       0.             1.3995  18.7812```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 23
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices PHI[2:2]
Symmetric Matrix
Constant Model Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                     COL1                 COL2

ROW1        37.499               37.501
0.000  0.220         0.000 -0.110

ROW2        37.501               37.503
0.000 -0.110         0.000  0.220
```
```             Rank order of 3 largest Lagrange multipliers in PHI
```
```               ROW2 : COL2         ROW2 : COL1         ROW1 : COL1
37.5034 : 0.000     37.5013 : 0.000     37.4993 : 0.000

```
```               Lagrange Multiplier and Wald Test Indices F[4:2]
Lower Triangular Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                    COL1                  COL2

X1        729.973   [Z1]          0.120
0.729 -0.120

X2        729.973   [Z1]          0.120
0.729  0.120

Y1          0.069               908.988   [Z3]
0.793 -0.079

Y2          0.069               908.988   [Z3]
0.792  0.079```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 24
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Rank order of 4 largest Lagrange multipliers in F
```
```                 X1 : COL2           X2 : COL2           Y2 : COL1
0.1201 : 0.729      0.1198 : 0.729      0.0692 : 0.792

Y1 : COL1
0.0690 : 0.793

```
```               Lagrange Multiplier and Wald Test Indices U[4:4]
Diagonal Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                 COL1               COL2               COL3               COL4

X1    443.950  [EPS1]     37.493             11.326              2.914
0.000  11.352      0.001  -5.150      0.088  -2.612

X2     37.493            443.950  [EPS1]      2.827              3.435
0.000  11.352                         0.093  -2.573      0.064  -2.836

Y1     11.326              2.827            352.733  [EPS3]     37.514
0.001  -5.150      0.093  -2.573                         0.000  15.666

Y2      2.914              3.435             37.514            352.733  [EPS3]
0.088  -2.612      0.064  -2.836      0.000  15.666
```
```              Rank order of 6 largest Lagrange multipliers in U
```
```                 Y2 : COL3           X2 : COL1           Y1 : COL1
37.5144 : 0.000     37.4932 : 0.000     11.3257 : 0.001

Y2 : COL2           Y2 : COL1           Y1 : COL2
3.4353 : 0.064      2.9138 : 0.088      2.8273 : 0.093

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 25
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Univariate Lagrange Multiplier Test
For Releasing Equality Constraints
------------------------------------------------------------
Chi-Square    Prob          Change       Parameter Equal to
------------------------------------------------------------```
```             0.119951   0.7291  -0.0601 =   0.0597  F[1:1]  = F[2:1]
0.069131   0.7926  -0.0396 =   0.0397  F[3:2]  = F[4:2]
0.552415   0.4573   1.2260 =  -1.2246  U[1:1]  = U[2:2]
0.242177   0.6226   0.7803 =  -0.7821  U[3:3]  = U[4:4]

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 26
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

LINEQS Model Statement
-------------------------------
Matrix         Rows & Cols          Matrix Type```
``` TERM   1-----------------------------------------------------------
1    _SEL_          4      10    SELECTION
2    _BETA_        10      10    EQSBETA        IMINUSINV
3    _GAMMA_       10       6    EQSGAMMA
4    _PHI_          6       6    SYMMETRIC

```
```     Number of endogenous variables = 4
```
```Manifest:     X1        X2        Y1        Y2

```
```     Number of exogenous variables = 6
```
```Latent:       F1        F2
Error:        E1        E2        E3        E4
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 27
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

Manifest Variable Equations
Initial Estimates```
```                      X1      =     .    *F1 + 1.0000 E1
Z1

X2      =     .    *F1 + 1.0000 E2
Z1

Y1      =     .    *F2 + 1.0000 E3
Z3

Y2      =     .    *F2 + 1.0000 E4
Z3

```
```                      Variances of Exogenous Variables
-------------------------------------
Variable    Parameter      Estimate
-------------------------------------```
```                    F1                           1.000000
F2                           1.000000
E1          EPS1                    .
E2          EPS1                    .
E3          EPS3                    .
E4          EPS3                    .

```
```                     Covariances among Exogenous Variables
--------------------------------
Parameter          Estimate
--------------------------------```
```                       F2    F1                1.000000
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 28
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          1
4 Variables          Model Matrices       4
10 Informations       Parameters           4

VARIABLE              Mean           Std Dev

X1                       0       9.295047068
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942
```
```
Covariances
```
```                    X1                X2                Y1                Y2

X1       86.39790000       57.77510000       56.86510000       58.89860000
X2       57.77510000       86.26320000       59.31770000       59.66830000
Y1       56.86510000       59.31770000       97.28500000       73.82010000
Y2       58.89860000       59.66830000       73.82010000       97.81920000
Determinant = 7377416 (Ln = 15.814)

Some initial estimates computed by instrumental variable method.

```
```                         Vector of Initial Estimates
```
```    Z1            1    7.60115  Matrix Entry: _GAMMA_[1:1] _GAMMA_[2:1]
Z3            2    8.59190  Matrix Entry: _GAMMA_[3:2] _GAMMA_[4:2]
EPS1          3   28.55302  Matrix Entry: _PHI_[3:3] _PHI_[4:4]
EPS3          4   23.73136  Matrix Entry: _PHI_[5:5] _PHI_[6:6]

```
```
Predetermined Elements of the Predicted Moment Matrix
```
```                    X1                X2                Y1                Y2

X1                 .                 .                 .                 .
X2                 .                 .                 .                 .
Y1                 .                 .                 .                 .
Y2                 .                 .                 .                 .
Sum of Squared Differences = 0```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 29
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 4
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 0.098
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    2   0    0.0578   0.0404 0.00198       0   0.910
2    0    3   0    0.0576 0.000208 0.00046       0   1.311
3    0    4   0    0.0576  0.00002 0.00014       0   1.308
4    0    5   0    0.0576 1.859E-6 0.00004       0   1.306
5    0    6   0    0.0576  1.74E-7 0.00001       0   1.306
6    0    7   0    0.0576 1.625E-8 4.06E-6       0   1.306

Optimization Results: Iterations= 6 Function Calls= 8 Jacobian Calls= 7
Active Constraints= 0  Criterion= 0.057613719
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                 30
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.33055005       51.64190292       60.66598749       60.66598749
X2       51.64190292       86.33055005       60.66598749       60.66598749
Y1       60.66598749       60.66598749       97.55210003       71.26697179
Y2       60.66598749       60.66598749       71.26697179       97.55210003
Determinant = 7814939 (Ln = 15.872)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 31
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0576
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9705
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9509
Root Mean Square Residual (RMR) . . . . . . . . .     2.5430
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.9705
Chi-square = 37.3337       df = 6       Prob>chi**2 = 0.0001
Null Model Chi-square:     df = 6                  1466.5524
RMSEA Estimate  . . . . . .  0.0898  90%C.I.[0.0635, 0.1184]
Probability of Close Fit  . . . . . . . . . . . .     0.0076
ECVI Estimate . . . . . . .  0.0701  90%C.I.[0.0458, 0.1059]
Bentler's Comparative Fit Index . . . . . . . . .     0.9785
Normal Theory Reweighted LS Chi-square  . . . . .    39.3380
Akaike's Information Criterion. . . . . . . . . .    25.3337
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .    -7.5189
Schwarz's Bayesian Criterion. . . . . . . . . . .    -1.5189
McDonald's (1989) Centrality. . . . . . . . . . .     0.9761
Bentler & Bonett's (1980) Non-normed Index. . . .     0.9785
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9745
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.9745
Z-Test of Wilson & Hilferty (1931). . . . . . . .     4.5535
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9745
Bollen (1988) Non-normed Index Delta2 . . . . . .     0.9785
Hoelter's (1983) Critical N . . . . . . . . . . .        220
```
`WARNING: The central parameter matrix _PHI_ has probably 1 zero eigenvalue(s).`

```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.067349949       6.133197083      -3.800887493      -1.767387493
X2       6.133197083      -0.067350051      -1.348287493      -0.997687493
Y1      -3.800887493      -1.348287493      -0.267100032       2.553128207
Y2      -1.767387493      -0.997687493       2.553128207       0.267099968
Average Absolute Residual = 1.727
Average Off-diagonal Absolute Residual = 2.767
```
```                      Rank Order of 5 Largest Residuals
```
```                   X2,X1     Y1,X1     Y2,Y1     Y2,X1     Y1,X2
6.1332   -3.8009    2.5531   -1.7674   -1.3483

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 32
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Asymptotically Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.024781917       6.122658111      -1.873789556      -0.871299725
X2       6.122658111      -0.024781955      -0.664688715      -0.491847340
Y1      -1.873789556      -0.664688715      -0.102069418       6.125849260
Y2      -0.871299725      -0.491847340       6.125849260       0.102069394
Average Standardized Residual = 1.64
Average Off-diagonal Standardized Residual = 2.692
```
```        Rank Order of 5 Largest Asymptotically Standardized Residuals
```
```                   Y2,Y1     X2,X1     Y1,X1     Y2,X1     Y1,X2
6.1258    6.1227   -1.8738   -0.8713   -0.6647

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 33
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Distribution of Asymptotically Standardized Residuals
(Each * represents 1 residuals)
```
```                     -2.00000 -   -1.75000  1  10.00% | *
-1.75000 -   -1.50000  0   0.00% |
-1.50000 -   -1.25000  0   0.00% |
-1.25000 -   -1.00000  0   0.00% |
-1.00000 -   -0.75000  1  10.00% | *
-0.75000 -   -0.50000  1  10.00% | *
-0.50000 -   -0.25000  1  10.00% | *
-0.25000 -          0  2  20.00% | **
0 -    0.25000  2  20.00% | **
0.25000 -    0.50000  0   0.00% |
0.50000 -    0.75000  0   0.00% |
0.75000 -    1.00000  0   0.00% |
1.00000 -    1.25000  0   0.00% |
1.25000 -    1.50000  0   0.00% |
1.50000 -    1.75000  0   0.00% |
1.75000 -    2.00000  0   0.00% |
2.00000 -    2.25000  0   0.00% |
2.25000 -    2.50000  0   0.00% |
2.50000 -    2.75000  0   0.00% |
2.75000 -    3.00000  0   0.00% |
3.00000 -    3.25000  0   0.00% |
3.25000 -    3.50000  0   0.00% |
3.50000 -    3.75000  0   0.00% |
3.75000 -    4.00000  0   0.00% |
4.00000 -    4.25000  0   0.00% |
4.25000 -    4.50000  0   0.00% |
4.50000 -    4.75000  0   0.00% |
4.75000 -    5.00000  0   0.00% |
5.00000 -    5.25000  0   0.00% |
5.25000 -    5.50000  0   0.00% |
5.50000 -    5.75000  0   0.00% |
5.75000 -    6.00000  0   0.00% |
6.00000 -    6.25000  2  20.00% | **
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 34
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Manifest Variable Equations```
```                     X1      =     7.1862*F1 +  1.0000 E1
Std Err       0.2660 Z1
t Value      27.0180

X2      =     7.1862*F1 +  1.0000 E2
Std Err       0.2660 Z1
t Value      27.0180

Y1      =     8.4420*F2 +  1.0000 E3
Std Err       0.2800 Z3
t Value      30.1494

Y2      =     8.4420*F2 +  1.0000 E4
Std Err       0.2800 Z3
t Value      30.1494

```
```                      Variances of Exogenous Variables
---------------------------------------------------------------------
Standard
Variable    Parameter      Estimate          Error          t Value
---------------------------------------------------------------------```
```    F1                           1.000000               0           0.000
F2                           1.000000               0           0.000
E1          EPS1            34.688647        1.646345          21.070
E2          EPS1            34.688647        1.646345          21.070
E3          EPS3            26.285128        1.399545          18.781
E4          EPS3            26.285128        1.399545          18.781

```
```                    Covariances among Exogenous Variables
----------------------------------------------------------------
Standard
Parameter          Estimate          Error          t Value
----------------------------------------------------------------```
```       F2    F1                1.000000               0           0.000
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 35
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Equations with Standardized Coefficients```
```                      X1      =    0.7734*F1 + 0.6339 E1
Z1

X2      =    0.7734*F1 + 0.6339 E2
Z1

Y1      =    0.8547*F2 + 0.5191 E3
Z3

Y2      =    0.8547*F2 + 0.5191 E4
Z3

```
```                         Squared Multiple Correlations
----------------------------------------------------------
Error           Total
Variable       Variance        Variance        R-squared
----------------------------------------------------------```
```             1    X1       34.688647       86.330550        0.598188
2    X2       34.688647       86.330550        0.598188
3    Y1       26.285128       97.552100        0.730553
4    Y2       26.285128       97.552100        0.730553

```
```                    Correlations among Exogenous Variables
--------------------------------
Parameter          Estimate
--------------------------------```
```                       F2    F1                1.000000

```
```
Predicted Moments of Latent Variables
```
```                                      F1                F2

F1       1.000000000       1.000000000
F2       1.000000000       1.000000000```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 36
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Moments between Manifest and Latent Variables
```
```                                      F1                F2

X1       7.186230091       7.186230091
X2       7.186230091       7.186230091
Y1       8.441976770       8.441976770
Y2       8.441976770       8.441976770
```
```
Latent Variable Score Regression Coefficients
```
```                                      F1                F2

X1      0.0220385544      0.0220385544
X2      0.0220385544      0.0220385544
Y1      0.0341667288      0.0341667288
Y2      0.0341667288      0.0341667288
```
```
Total Effects of Exogenous on Endogenous Variables
```
```                                      F1                F2

X1       7.186230091       0.000000000
X2       7.186230091       0.000000000
Y1       0.000000000       8.441976770
Y2       0.000000000       8.441976770
```
```
Indirect Effects of Exogenous on Endogenous Variables
```
```                                      F1                F2

X1                 0                 0
X2                 0                 0
Y1                 0                 0
Y2                 0                 0
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 37
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices _PHI_[6:6]
Symmetric Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                          F1                     F2                     E1

F1         37.499                 37.501                 21.389
0.000   0.220          0.000  -0.110          0.000   0.793

F2         37.501                 37.503                 21.473
0.000  -0.110          0.000   0.220          0.000  -0.767

E1         21.389                 21.473                443.949  [EPS1]
0.000   0.793          0.000  -0.767

E2         12.349                 10.429                 37.493
0.000   0.602          0.001  -0.535          0.000  11.352

E3         15.615                 13.301                 11.326
0.000  -0.659          0.000   0.583          0.001  -5.150

E4          7.772                  7.900                  2.914
0.005  -0.465          0.005   0.449          0.088  -2.612

E2                     E3                     E4

F1         12.349                 15.615                  7.772
0.000   0.602          0.000  -0.659          0.005  -0.465

F2         10.429                 13.301                  7.900
0.001  -0.535          0.000   0.583          0.005   0.449

E1         37.493                 11.326                  2.914
0.000  11.352          0.001  -5.150          0.088  -2.612

E2        443.949  [EPS1]          2.827                  3.435
0.093  -2.573          0.064  -2.836

E3          2.827                352.733  [EPS3]         37.515
0.093  -2.573                                 0.000  15.666

E4          3.435                 37.515                352.733  [EPS3]
0.064  -2.836          0.000  15.666```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 38
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Rank order of 10 largest Lagrange multipliers in _PHI_
```
```                 E4 : E3             F2 : F2             F2 : F1
37.5148 : 0.000     37.5035 : 0.000     37.5014 : 0.000

F1 : F1             E2 : E1             E1 : F2
37.4993 : 0.000     37.4931 : 0.000     21.4730 : 0.000

E1 : F1             E3 : F1             E3 : F2
21.3891 : 0.000     15.6148 : 0.000     13.3009 : 0.000

E2 : F1
12.3485 : 0.000

```
```            Lagrange Multiplier and Wald Test Indices _GAMMA_[4:2]
General Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                      F1                    F2

X1        729.973   [Z1]          0.120
0.729 -0.120

X2        729.973   [Z1]          0.120
0.729  0.120

Y1          0.069               908.988   [Z3]
0.793 -0.079

Y2          0.069               908.988   [Z3]
0.792  0.079
```
```           Rank order of 4 largest Lagrange multipliers in _GAMMA_
```
```                 X1 : F2             X2 : F2             Y2 : F1
0.1201 : 0.729      0.1198 : 0.729      0.0692 : 0.792

Y1 : F1
0.0690 : 0.793

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 39
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 1, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Univariate Lagrange Multiplier Test
For Releasing Equality Constraints
------------------------------------------------------------
Chi-Square    Prob          Change       Parameter Equal to
------------------------------------------------------------```
```             0.119951   0.7291  -0.0602 =   0.0597  [X1:F1] = [X2:F1]
0.069131   0.7926  -0.0396 =   0.0397  [Y1:F2] = [Y2:F2]
0.552415   0.4573   1.2260 =  -1.2246  [E1:E1] = [E2:E2]
0.242176   0.6226   0.7803 =  -0.7821  [E3:E3] = [E4:E4]

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 40
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

FACTOR Model Statement
-------------------------------
Matrix         Rows & Cols          Matrix Type```
``` TERM   1-----------------------------------------------------------
1    _F_            4       2    GENERAL
2    _P_            2       2    SYMMETRIC
TERM   2-----------------------------------------------------------
3    _U_            4       4    SYMMETRIC

```
```                      Initial Parameter Matrix _P_[2:2]
Symmetric Matrix```
```                                    FCOR1           FCOR2

FCOR1        1.00             .  [RO]
FCOR2         .  [RO]        1.00
```
```                      Initial Parameter Matrix _F_[4:2]
Lower Triangular Matrix```
```                                   FACT1           FACT2

X1         .  [Z1]          .0
X2         .  [Z1]          .0
Y1          .0             .  [Z3]
Y2          .0             .  [Z3]
```
```                      Initial Parameter Matrix _U_[4:4]
Diagonal Matrix```
```                 UVAR1             UVAR2             UVAR3             UVAR4

X1         .  [EPS1]          .0                .0                .0
X2          .0               .  [EPS1]          .0                .0
Y1          .0                .0               .  [EPS3]          .0
Y2          .0                .0                .0               .  [EPS3]```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 41
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```     Covariance Structure Analysis: ULS and Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          2
4 Variables          Model Matrices       3
10 Informations       Parameters           5

VARIABLE              Mean           Std Dev

X1                       0       9.295047068
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942
```
```
Covariances
```
```                    X1                X2                Y1                Y2

X1       86.39790000       57.77510000       56.86510000       58.89860000
X2       57.77510000       86.26320000       59.31770000       59.66830000
Y1       56.86510000       59.31770000       97.28500000       73.82010000
Y2       58.89860000       59.66830000       73.82010000       97.81920000
Determinant = 7377416 (Ln = 15.814)

Some initial estimates computed by McDonald's method.

```
```                         Vector of Initial Estimates
```
```          Z1            1    8.48839  Matrix Entry: _F_[1:1] _F_[2:1]
Z3            2    9.25668  Matrix Entry: _F_[3:2] _F_[4:2]
RO            3    0.74690  Matrix Entry: _P_[2:1]
EPS1          4   14.27773  Matrix Entry: _U_[1:1] _U_[2:2]
EPS3          5   11.86602  Matrix Entry: _U_[3:3] _U_[4:4]

```
```
Predetermined Elements of the Predicted Moment Matrix
```
```                    X1                X2                Y1                Y2

X1                 .                 .                 .                 .
X2                 .                 .                 .                 .
Y1                 .                 .                 .                 .
Y2                 .                 .                 .                 .
Sum of Squared Differences = 0```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 42
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 5
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 349.456
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    2   0   11.8258    337.6   628.5       0   0.980
2    0    3   0    4.8015   7.0243   7.307       0   1.000
3    0    4   0    4.8007 0.000792 0.00018       0   1.000
4    0    5   0    4.8007 4.57E-13 371E-14       0   1.002

Optimization Results: Iterations= 4 Function Calls= 6 Jacobian Calls= 5
Active Constraints= 0  Criterion= 4.8007041
```
`NOTE:  GCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                 43
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.33055000       57.77510000       58.68742500       58.68742500
X2       57.77510000       86.33055000       58.68742500       58.68742500
Y1       58.68742500       58.68742500       97.55210000       73.82010000
Y2       58.68742500       58.68742500       73.82010000       97.55210000
Determinant = 7399462 (Ln = 15.817)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 44
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     4.8007
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9999
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9998
Root Mean Square Residual (RMR) . . . . . . . . .     0.6983
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.8332

```
```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.067350000       0.000000000      -1.822325000       0.211175000
X2       0.000000000      -0.067350000       0.630275000       0.980875000
Y1      -1.822325000       0.630275000      -0.267100000       0.000000000
Y2       0.211175000       0.980875000       0.000000000       0.267100000
Average Absolute Residual = 0.4314
Average Off-diagonal Absolute Residual = 0.6074
```
```                      Rank Order of 5 Largest Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y2,Y2     Y1,Y1
-1.8223    0.9809    0.6303    0.2671   -0.2671

```
```
Variance Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1      0.0007795328      0.0000000000      -.0198770211      0.0022970945
X2      0.0000000000      -.0007807501      0.0068800938      0.0106779733
Y1      -.0198770211      0.0068800938      -.0027455415      0.0000000000
Y2      0.0022970945      0.0106779733      0.0000000000      0.0027305478
Average Standardized Residual = 0.004677
Average Off-diagonal Standardized Residual = 0.006622
```
```           Rank Order of 5 Largest Variance Standardized Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y1,Y1     Y2,Y2
-0.0199    0.0107  0.006880 -0.002746  0.002731

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 45
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation

Distribution of Variance Standardized Residuals
(Each * represents 1 residuals)
```
```                    -0.02037 -   -0.01528  1  10.00% | *
-0.01528 -   -0.01018  0   0.00% |
-0.01018 -   -0.00509  0   0.00% |
-0.00509 -          0  2  20.00% | **
0 -    0.00509  5  50.00% | *****
0.00509 -    0.01018  1  10.00% | *
0.01018 -    0.01528  1  10.00% | *

```
```                     Estimated Parameter Matrix _P_[2:2]
Symmetric Matrix```
```                                    FCOR1             FCOR2

FCOR1        1.0000            0.8986[RO]
FCOR2        0.8986[RO]        1.0000
```
```                     Estimated Parameter Matrix _F_[4:2]
Lower Triangular Matrix```
```                                   FACT1             FACT2

X1        7.6010[Z1]        0.
X2        7.6010[Z1]        0.
Y1        0.                8.5919[Z3]
Y2        0.                8.5919[Z3]
```
```                     Estimated Parameter Matrix _U_[4:4]
Diagonal Matrix```
```                UVAR1              UVAR2              UVAR3              UVAR4

X1      28.5554[EPS1]       0.                 0.                 0.
X2       0.                28.5554[EPS1]       0.                 0.
Y1       0.                 0.                23.7320[EPS3]       0.
Y2       0.                 0.                 0.                23.7320[EPS3]```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 46
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation

```
```                                   FACT1             FACT2

X1      0.8180655402      0.0000000000
X2      0.8180655402      0.0000000000
Y1      0.0000000000      0.8698993436
Y2      0.0000000000      0.8698993436
```
```                        Squared Multiple Correlations
-------------------------------------------------------------
Error           Total
Parameter        Variance        Variance        R-squared
-------------------------------------------------------------```
```           1    X1          28.555450       86.330550        0.669231
2    X2          28.555450       86.330550        0.669231
3    Y1          23.732000       97.552100        0.756725
4    Y2          23.732000       97.552100        0.756725

```
```                    Correlations among Exogenous Variables
------------------------------------------------------
Row & Column          Parameter             Estimate
------------------------------------------------------```
```               2       1    FCOR2    FCOR1    RO          0.898643

```
```
Factor Score Regression Coefficients
```
```                                   FACT1             FACT2

X1      0.0044362131      0.0021870286
X2      0.0044362131      0.0021870286
Y1      0.0015231726      0.0035781603
Y2      0.0015231726      0.0035781603
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 47
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 5
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 0.003
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```Optimization Results: Iterations= 0 Function Calls= 2 Jacobian Calls= 1
Active Constraints= 0  Criterion= 0.0029838497
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                 48
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.33055000       57.77510000       58.68742500       58.68742500
X2       57.77510000       86.33055000       58.68742500       58.68742500
Y1       58.68742500       58.68742500       97.55210000       73.82010000
Y2       58.68742500       58.68742500       73.82010000       97.55210000
Determinant = 7399462 (Ln = 15.817)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 49
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0030
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9985
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9970
Root Mean Square Residual (RMR) . . . . . . . . .     0.6983
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.8321
Chi-square = 1.9335        df = 5       Prob>chi**2 = 0.8583
Null Model Chi-square:     df = 6                  1466.5524
RMSEA Estimate  . . . . . . . . . 0.0000  90%C.I.[., 0.0293]
Probability of Close Fit  . . . . . . . . . . . .     0.9936
ECVI Estimate . . . . . . . . . . 0.0185  90%C.I.[., 0.0276]
Bentler's Comparative Fit Index . . . . . . . . .     1.0000
Normal Theory Reweighted LS Chi-square  . . . . .     1.9568
Akaike's Information Criterion. . . . . . . . . .    -8.0665
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .   -35.4436
Schwarz's Bayesian Criterion. . . . . . . . . . .   -30.4436
McDonald's (1989) Centrality. . . . . . . . . . .     1.0024
Bentler & Bonett's (1980) Non-normed Index. . . .     1.0025
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9987
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.8322
Z-Test of Wilson & Hilferty (1931). . . . . . . .    -1.0768
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9984
Bollen (1988) Non-normed Index Delta2 . . . . . .     1.0021
Hoelter's (1983) Critical N . . . . . . . . . . .       3712

```
```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.067350000       0.000000000      -1.822325000       0.211175000
X2       0.000000000      -0.067350000       0.630275000       0.980875000
Y1      -1.822325000       0.630275000      -0.267100000       0.000000000
Y2       0.211175000       0.980875000       0.000000000       0.267100000
Average Absolute Residual = 0.4314
Average Off-diagonal Absolute Residual = 0.6074
```
```                      Rank Order of 5 Largest Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y2,Y2     Y1,Y1
-1.8223    0.9809    0.6303    0.2671   -0.2671

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 50
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Asymptotically Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1      0.0267263773      0.0000000000      -.9784404931      0.1133838207
X2      0.0000000000      -.0267263773      0.3384064762      0.5266501961
Y1      -.9784404931      0.3384064762      -.1066164052      0.0000000000
Y2      0.1133838207      0.5266501961      0.0000000000      0.1066164052
Average Standardized Residual = 0.2224
Average Off-diagonal Standardized Residual = 0.3261
```
```        Rank Order of 5 Largest Asymptotically Standardized Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y2,X1     Y2,Y2
-0.9784    0.5267    0.3384    0.1134    0.1066

```
```            Distribution of Asymptotically Standardized Residuals
(Each * represents 1 residuals)
```
```                    -1.00000 -   -0.75000  1  10.00% | *
-0.75000 -   -0.50000  0   0.00% |
-0.50000 -   -0.25000  0   0.00% |
-0.25000 -          0  2  20.00% | **
0 -    0.25000  5  50.00% | *****
0.25000 -    0.50000  1  10.00% | *
0.50000 -    0.75000  1  10.00% | *

```
```                     Estimated Parameter Matrix _P_[2:2]
Standard Errors and t Values
Symmetric Matrix```
```                                    FCOR1                  FCOR2

FCOR1        1.0000                 0.8986     [RO]
0.       0.            0.0187  48.1801

FCOR2        0.8986     [RO]        1.0000
0.0187  48.1801        0.       0.```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 51
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix _F_[4:2]
Standard Errors and t Values
Lower Triangular Matrix```
```                                   FACT1                  FACT2

X1        7.6010     [Z1]        0.
0.2684  28.3158        0.       0.

X2        7.6010     [Z1]        0.
0.2684  28.3158        0.       0.

Y1        0.                     8.5919     [Z3]
0.       0.            0.2797  30.7215

Y2        0.                     8.5919     [Z3]
0.       0.            0.2797  30.7215
```
```                     Estimated Parameter Matrix _U_[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                   UVAR1                   UVAR2

X1        28.5554   [EPS1]         0.
1.5864  18.0000         0.       0.

X2         0.                     28.5554   [EPS1]
0.       0.             1.5864  18.0000

Y1         0.                      0.
0.       0.             0.       0.

Y2         0.                      0.
0.       0.             0.       0.```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 52
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix _U_[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                   UVAR3                   UVAR4

X1         0.                      0.
0.       0.             0.       0.

X2         0.                      0.
0.       0.             0.       0.

Y1        23.7320   [EPS3]         0.
1.3184  18.0000         0.       0.

Y2         0.                     23.7320   [EPS3]
0.       0.             1.3184  18.0000```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 53
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

```
```                                   FACT1             FACT2

X1      0.8180655402      0.0000000000
X2      0.8180655402      0.0000000000
Y1      0.0000000000      0.8698993436
Y2      0.0000000000      0.8698993436
```
```                        Squared Multiple Correlations
-------------------------------------------------------------
Error           Total
Parameter        Variance        Variance        R-squared
-------------------------------------------------------------```
```           1    X1          28.555450       86.330550        0.669231
2    X2          28.555450       86.330550        0.669231
3    Y1          23.732000       97.552100        0.756725
4    Y2          23.732000       97.552100        0.756725

```
```                    Correlations among Exogenous Variables
------------------------------------------------------
Row & Column          Parameter             Estimate
------------------------------------------------------```
```               2       1    FCOR2    FCOR1    RO          0.898643

```
```
Factor Score Regression Coefficients
```
```                                   FACT1             FACT2

X1      0.0044362131      0.0021870286
X2      0.0044362131      0.0021870286
Y1      0.0015231726      0.0035781603
Y2      0.0015231726      0.0035781603
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 54
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices _P_[2:2]
Symmetric Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                    FCOR1                  FCOR2

FCOR1            SING               2321.323   [RO]
.      .

FCOR2        2321.323   [RO]            SING
.      .
```
```              Lagrange Multiplier and Wald Test Indices _F_[4:2]
Lower Triangular Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                   FACT1                 FACT2

X1        801.785   [Z1]          0.205
0.651 -0.143

X2        801.785   [Z1]          0.205
0.651  0.143

Y1          0.150               943.808   [Z3]
0.699 -0.113

Y2          0.150               943.808   [Z3]
0.699  0.113
```
```             Rank order of 4 largest Lagrange multipliers in _F_
```
```                 X1 : FACT2          X2 : FACT2          Y1 : FACT1
0.2050 : 0.651      0.2050 : 0.651      0.1497 : 0.699

Y2 : FACT1
0.1497 : 0.699

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 55
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices _U_[4:4]
Diagonal Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                UVAR1              UVAR2              UVAR3              UVAR4

X1     324.000 [EPS1]        SING              1.789              0.323
.      .          0.181 -2.061       0.570  0.876

X2        SING            324.000 [EPS1]       0.451              0.010
.      .                             0.502  1.034       0.922  0.151

Y1       1.789              0.451            324.000 [EPS3]        SING
0.181 -2.061       0.502  1.034                           .      .

Y2       0.323              0.010               SING            324.000 [EPS3]
0.570  0.876       0.922  0.151        .      .
```
```             Rank order of 4 largest Lagrange multipliers in _U_
```
```                 Y1 : UVAR1          Y1 : UVAR2          Y2 : UVAR1
1.7894 : 0.181      0.4505 : 0.502      0.3235 : 0.570

Y2 : UVAR2
0.00955 : 0.922

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 56
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Univariate Lagrange Multiplier Test
For Releasing Equality Constraints
-------------------------------------------------------------
Chi-Square    Prob          Change       Parameter  Equal to
-------------------------------------------------------------```
```            0.047575   0.8273  -0.0348 =   0.0348  _F_[1:1]= _F_[2:1]
0.049417   0.8241  -0.0319 =   0.0319  _F_[3:2]= _F_[4:2]
0.488258   0.4847   1.1708 =  -1.1708  _U_[1:1]= _U_[2:2]
0.178518   0.6726   0.7038 =  -0.7038  _U_[3:3]= _U_[4:4]

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 57
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

COSAN Model Statement
-------------------------------
Matrix         Rows & Cols          Matrix Type```
``` TERM   1-----------------------------------------------------------
1    F              4       2    GENERAL
2    PHI            2       2    SYMMETRIC
TERM   2-----------------------------------------------------------
3    U              4       4    DIAGONAL

```
```                      Initial Parameter Matrix PHI[2:2]
Symmetric Matrix```
```                                     COL1            COL2

ROW1        1.00             .  [RO]
ROW2         .  [RO]        1.00
```
```                       Initial Parameter Matrix F[4:2]
Lower Triangular Matrix```
```                                    COL1            COL2

X1         .  [Z1]          .0
X2         .  [Z1]          .0
Y1          .0             .  [Z3]
Y2          .0             .  [Z3]
```
```                       Initial Parameter Matrix U[4:4]
Diagonal Matrix```
```                  COL1              COL2              COL3              COL4

X1         .  [EPS1]          .0                .0                .0
X2          .0               .  [EPS1]          .0                .0
Y1          .0                .0               .  [EPS3]          .0
Y2          .0                .0                .0               .  [EPS3]```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 58
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```     Covariance Structure Analysis: ULS and Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          2
4 Variables          Model Matrices       3
10 Informations       Parameters           5

VARIABLE              Mean           Std Dev

X1                       0       9.295047068
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942
```
```
Covariances
```
```                    X1                X2                Y1                Y2

X1       86.39790000       57.77510000       56.86510000       58.89860000
X2       57.77510000       86.26320000       59.31770000       59.66830000
Y1       56.86510000       59.31770000       97.28500000       73.82010000
Y2       58.89860000       59.66830000       73.82010000       97.81920000
Determinant = 7377416 (Ln = 15.814)

```
```                         Vector of Initial Estimates
```
```          Z1            1    0.50000  Matrix Entry: F[1:1] F[2:1]
Z3            2    0.50000  Matrix Entry: F[3:2] F[4:2]
RO            3    0.50000  Matrix Entry: PHI[2:1]
EPS1          4   50.00000  Matrix Entry: U[1:1] U[2:2]
EPS3          5   50.00000  Matrix Entry: U[3:3] U[4:4]

```
```
Predetermined Elements of the Predicted Moment Matrix
```
```                    X1                X2                Y1                Y2

X1                 .                 .                 .                 .
X2                 .                 .                 .                 .
Y1                 .                 .                 .                 .
Y2                 .                 .                 .                 .
Sum of Squared Differences = 0```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 59
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 5
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 25984.023
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    4   0     11002  14981.9  5181.8  26.567   5.234
2    0    5   0      8884   2118.3  2753.6   3.882   0.980
3    0    6   0      6859   2025.0   404.7   0.522   0.994
4    0    7   0      5928    931.0  1190.4  0.0984   1.072
5    0    8   0      5090    838.4  2608.8  0.0543   0.487
6    0    9   0      1907   3182.8   767.8  0.0594   1.063
7    0   11   0      1395    512.0   602.1   0.171   1.039
8    0   12   0  648.7229    746.0   886.5  0.0599   1.034
9    0   13   0  268.7526    380.0  4107.0       0   0.590
10    0   14   0    5.2242    263.5   168.2       0   0.998
11    0   15   0    4.8007   0.4235   0.110       0   1.000
12    0   16   0    4.8007  1.78E-7 2.01E-8       0   1.000

Optimization Results: Iterations= 12 Function Calls= 17 Jacobian Calls= 13
Active Constraints= 0  Criterion= 4.8007041
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                 60
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.33055000       57.77510000       58.68742500       58.68742500
X2       57.77510000       86.33055000       58.68742500       58.68742500
Y1       58.68742500       58.68742500       97.55210000       73.82010000
Y2       58.68742500       58.68742500       73.82010000       97.55210000
Determinant = 7399462 (Ln = 15.817)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 61
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     4.8007
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9999
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9998
Root Mean Square Residual (RMR) . . . . . . . . .     0.6983
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.8332

```
```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.067350000       0.000000000      -1.822325000       0.211175000
X2       0.000000000      -0.067350000       0.630275000       0.980875000
Y1      -1.822325000       0.630275000      -0.267100000       0.000000000
Y2       0.211175000       0.980875000       0.000000000       0.267100000
Average Absolute Residual = 0.4314
Average Off-diagonal Absolute Residual = 0.6074
```
```                      Rank Order of 5 Largest Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y2,Y2     Y1,Y1
-1.8223    0.9809    0.6303    0.2671   -0.2671

```
```
Variance Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1      0.0007795328      0.0000000000      -.0198770211      0.0022970945
X2      0.0000000000      -.0007807501      0.0068800938      0.0106779733
Y1      -.0198770211      0.0068800938      -.0027455415      0.0000000000
Y2      0.0022970945      0.0106779733      0.0000000000      0.0027305478
Average Standardized Residual = 0.004677
Average Off-diagonal Standardized Residual = 0.006622
```
```           Rank Order of 5 Largest Variance Standardized Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y1,Y1     Y2,Y2
-0.0199    0.0107  0.006880 -0.002746  0.002731

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 62
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation

Distribution of Variance Standardized Residuals
(Each * represents 1 residuals)
```
```                    -0.02037 -   -0.01528  1  10.00% | *
-0.01528 -   -0.01018  0   0.00% |
-0.01018 -   -0.00509  0   0.00% |
-0.00509 -          0  2  20.00% | **
0 -    0.00509  5  50.00% | *****
0.00509 -    0.01018  1  10.00% | *
0.01018 -    0.01528  1  10.00% | *

```
```                     Estimated Parameter Matrix PHI[2:2]
Symmetric Matrix```
```                                     COL1              COL2

ROW1        1.0000            0.8986[RO]
ROW2        0.8986[RO]        1.0000
```
```                      Estimated Parameter Matrix F[4:2]
Lower Triangular Matrix```
```                                    COL1              COL2

X1        7.6010[Z1]        0.
X2        7.6010[Z1]        0.
Y1        0.                8.5919[Z3]
Y2        0.                8.5919[Z3]
```
```                      Estimated Parameter Matrix U[4:4]
Diagonal Matrix```
```                 COL1               COL2               COL3               COL4

X1      28.5554[EPS1]       0.                 0.                 0.
X2       0.                28.5554[EPS1]       0.                 0.
Y1       0.                 0.                23.7320[EPS3]       0.
Y2       0.                 0.                 0.                23.7320[EPS3]```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 63
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 5
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 0.003
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```Optimization Results: Iterations= 0 Function Calls= 2 Jacobian Calls= 1
Active Constraints= 0  Criterion= 0.0029838497
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                 64
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.33055000       57.77510000       58.68742500       58.68742500
X2       57.77510000       86.33055000       58.68742500       58.68742500
Y1       58.68742500       58.68742500       97.55210000       73.82010000
Y2       58.68742500       58.68742500       73.82010000       97.55210000
Determinant = 7399462 (Ln = 15.817)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 65
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0030
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9985
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9970
Root Mean Square Residual (RMR) . . . . . . . . .     0.6983
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.8321
Chi-square = 1.9335        df = 5       Prob>chi**2 = 0.8583
Null Model Chi-square:     df = 6                  1466.5524
RMSEA Estimate  . . . . . . . . . 0.0000  90%C.I.[., 0.0293]
Probability of Close Fit  . . . . . . . . . . . .     0.9936
ECVI Estimate . . . . . . . . . . 0.0185  90%C.I.[., 0.0276]
Bentler's Comparative Fit Index . . . . . . . . .     1.0000
Normal Theory Reweighted LS Chi-square  . . . . .     1.9568
Akaike's Information Criterion. . . . . . . . . .    -8.0665
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .   -35.4436
Schwarz's Bayesian Criterion. . . . . . . . . . .   -30.4436
McDonald's (1989) Centrality. . . . . . . . . . .     1.0024
Bentler & Bonett's (1980) Non-normed Index. . . .     1.0025
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9987
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.8322
Z-Test of Wilson & Hilferty (1931). . . . . . . .    -1.0768
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9984
Bollen (1988) Non-normed Index Delta2 . . . . . .     1.0021
Hoelter's (1983) Critical N . . . . . . . . . . .       3712

```
```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.067350000       0.000000000      -1.822325000       0.211175000
X2       0.000000000      -0.067350000       0.630275000       0.980875000
Y1      -1.822325000       0.630275000      -0.267100000       0.000000000
Y2       0.211175000       0.980875000       0.000000000       0.267100000
Average Absolute Residual = 0.4314
Average Off-diagonal Absolute Residual = 0.6074
```
```                      Rank Order of 5 Largest Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y2,Y2     Y1,Y1
-1.8223    0.9809    0.6303    0.2671   -0.2671

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 66
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Asymptotically Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1      0.0267263773      0.0000000000      -.9784404931      0.1133838208
X2      0.0000000000      -.0267263773      0.3384064762      0.5266501961
Y1      -.9784404931      0.3384064762      -.1066164052      0.0000000000
Y2      0.1133838208      0.5266501961      0.0000000000      0.1066164052
Average Standardized Residual = 0.2224
Average Off-diagonal Standardized Residual = 0.3261
```
```        Rank Order of 5 Largest Asymptotically Standardized Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y2,X1     Y2,Y2
-0.9784    0.5267    0.3384    0.1134    0.1066

```
```            Distribution of Asymptotically Standardized Residuals
(Each * represents 1 residuals)
```
```                    -1.00000 -   -0.75000  1  10.00% | *
-0.75000 -   -0.50000  0   0.00% |
-0.50000 -   -0.25000  0   0.00% |
-0.25000 -          0  2  20.00% | **
0 -    0.25000  5  50.00% | *****
0.25000 -    0.50000  1  10.00% | *
0.50000 -    0.75000  1  10.00% | *

```
```                     Estimated Parameter Matrix PHI[2:2]
Standard Errors and t Values
Symmetric Matrix```
```                                     COL1                   COL2

ROW1        1.0000                 0.8986     [RO]
0.       0.            0.0187  48.1801

ROW2        0.8986     [RO]        1.0000
0.0187  48.1801        0.       0.```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 67
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix F[4:2]
Standard Errors and t Values
Lower Triangular Matrix```
```                                    COL1                   COL2

X1        7.6010     [Z1]        0.
0.2684  28.3158        0.       0.

X2        7.6010     [Z1]        0.
0.2684  28.3158        0.       0.

Y1        0.                     8.5919     [Z3]
0.       0.            0.2797  30.7215

Y2        0.                     8.5919     [Z3]
0.       0.            0.2797  30.7215
```
```                      Estimated Parameter Matrix U[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                    COL1                    COL2

X1        28.5554   [EPS1]         0.
1.5864  18.0000         0.       0.

X2         0.                     28.5554   [EPS1]
0.       0.             1.5864  18.0000

Y1         0.                      0.
0.       0.             0.       0.

Y2         0.                      0.
0.       0.             0.       0.```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 68
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix U[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                    COL3                    COL4

X1         0.                      0.
0.       0.             0.       0.

X2         0.                      0.
0.       0.             0.       0.

Y1        23.7320   [EPS3]         0.
1.3184  18.0000         0.       0.

Y2         0.                     23.7320   [EPS3]
0.       0.             1.3184  18.0000```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 69
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices PHI[2:2]
Symmetric Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                     COL1                   COL2

ROW1            SING               2321.323   [RO]
.      .

ROW2        2321.323   [RO]            SING
.      .
```
```               Lagrange Multiplier and Wald Test Indices F[4:2]
Lower Triangular Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                    COL1                  COL2

X1        801.785   [Z1]          0.205
0.651 -0.143

X2        801.785   [Z1]          0.205
0.651  0.143

Y1          0.150               943.808   [Z3]
0.699 -0.113

Y2          0.150               943.808   [Z3]
0.699  0.113
```
```              Rank order of 4 largest Lagrange multipliers in F
```
```                 X2 : COL2           X1 : COL2           Y2 : COL1
0.2050 : 0.651      0.2050 : 0.651      0.1497 : 0.699

Y1 : COL1
0.1497 : 0.699

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 70
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices U[4:4]
Diagonal Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                 COL1               COL2               COL3               COL4

X1     324.000 [EPS1]        SING              1.789              0.323
.      .          0.181 -2.061       0.570  0.876

X2        SING            324.000 [EPS1]       0.451              0.010
.      .                             0.502  1.034       0.922  0.151

Y1       1.789              0.451            324.000 [EPS3]        SING
0.181 -2.061       0.502  1.034                           .      .

Y2       0.323              0.010               SING            324.000 [EPS3]
0.570  0.876       0.922  0.151        .      .
```
```              Rank order of 4 largest Lagrange multipliers in U
```
```                 Y1 : COL1           Y1 : COL2           Y2 : COL1
1.7894 : 0.181      0.4505 : 0.502      0.3235 : 0.570

Y2 : COL2
0.00955 : 0.922

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 71
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Univariate Lagrange Multiplier Test
For Releasing Equality Constraints
------------------------------------------------------------
Chi-Square    Prob          Change       Parameter Equal to
------------------------------------------------------------```
```             0.047575   0.8273  -0.0348 =   0.0348  F[1:1]  = F[2:1]
0.049417   0.8241  -0.0319 =   0.0319  F[3:2]  = F[4:2]
0.488258   0.4847   1.1708 =  -1.1708  U[1:1]  = U[2:2]
0.178518   0.6726   0.7038 =  -0.7038  U[3:3]  = U[4:4]

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 72
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

LINEQS Model Statement
-------------------------------
Matrix         Rows & Cols          Matrix Type```
``` TERM   1-----------------------------------------------------------
1    _SEL_          4      10    SELECTION
2    _BETA_        10      10    EQSBETA        IMINUSINV
3    _GAMMA_       10       6    EQSGAMMA
4    _PHI_          6       6    SYMMETRIC

```
```     Number of endogenous variables = 4
```
```Manifest:     X1        X2        Y1        Y2

```
```     Number of exogenous variables = 6
```
```Latent:       F1        F2
Error:        E1        E2        E3        E4
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 73
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

Manifest Variable Equations
Initial Estimates```
```                      X1      =     .    *F1 + 1.0000 E1
Z1

X2      =     .    *F1 + 1.0000 E2
Z1

Y1      =     .    *F2 + 1.0000 E3
Z3

Y2      =     .    *F2 + 1.0000 E4
Z3

```
```                      Variances of Exogenous Variables
-------------------------------------
Variable    Parameter      Estimate
-------------------------------------```
```                    F1                           1.000000
F2                           1.000000
E1          EPS1                    .
E2          EPS1                    .
E3          EPS3                    .
E4          EPS3                    .

```
```                     Covariances among Exogenous Variables
--------------------------------
Parameter          Estimate
--------------------------------```
```                       F2    F1    RO                 .
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 74
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```     Covariance Structure Analysis: ULS and Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          1
4 Variables          Model Matrices       4
10 Informations       Parameters           5

VARIABLE              Mean           Std Dev

X1                       0       9.295047068
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942
```
```
Covariances
```
```                    X1                X2                Y1                Y2

X1       86.39790000       57.77510000       56.86510000       58.89860000
X2       57.77510000       86.26320000       59.31770000       59.66830000
Y1       56.86510000       59.31770000       97.28500000       73.82010000
Y2       58.89860000       59.66830000       73.82010000       97.81920000
Determinant = 7377416 (Ln = 15.814)

Some initial estimates computed by instrumental variable method.

```
```                         Vector of Initial Estimates
```
```    Z1            1    7.60115  Matrix Entry: _GAMMA_[1:1] _GAMMA_[2:1]
Z3            2    8.59190  Matrix Entry: _GAMMA_[3:2] _GAMMA_[4:2]
RO            3    0.89868  Matrix Entry: _PHI_[2:1]
EPS1          4   28.55302  Matrix Entry: _PHI_[3:3] _PHI_[4:4]
EPS3          5   23.73136  Matrix Entry: _PHI_[5:5] _PHI_[6:6]

```
```
Predetermined Elements of the Predicted Moment Matrix
```
```                    X1                X2                Y1                Y2

X1                 .                 .                 .                 .
X2                 .                 .                 .                 .
Y1                 .                 .                 .                 .
Y2                 .                 .                 .                 .
Sum of Squared Differences = 0```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 75
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 5
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 4.801
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    2   0    4.8007  0.00007 0.00004       0   1.000
2    0    3   0    4.8007 2.04E-14 122E-14       0   0.995

Optimization Results: Iterations= 2 Function Calls= 4 Jacobian Calls= 3
Active Constraints= 0  Criterion= 4.8007041
```
`NOTE:  GCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                 76
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.33055000       57.77510000       58.68742500       58.68742500
X2       57.77510000       86.33055000       58.68742500       58.68742500
Y1       58.68742500       58.68742500       97.55210000       73.82010000
Y2       58.68742500       58.68742500       73.82010000       97.55210000
Determinant = 7399462 (Ln = 15.817)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 77
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     4.8007
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9999
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9998
Root Mean Square Residual (RMR) . . . . . . . . .     0.6983
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.8332

```
```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.067350000       0.000000000      -1.822325000       0.211175000
X2       0.000000000      -0.067350000       0.630275000       0.980875000
Y1      -1.822325000       0.630275000      -0.267100000       0.000000000
Y2       0.211175000       0.980875000       0.000000000       0.267100000
Average Absolute Residual = 0.4314
Average Off-diagonal Absolute Residual = 0.6074
```
```                      Rank Order of 5 Largest Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y2,Y2     Y1,Y1
-1.8223    0.9809    0.6303    0.2671   -0.2671

```
```
Variance Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1      0.0007795328      0.0000000000      -.0198770211      0.0022970945
X2      0.0000000000      -.0007807501      0.0068800938      0.0106779733
Y1      -.0198770211      0.0068800938      -.0027455415      0.0000000000
Y2      0.0022970945      0.0106779733      0.0000000000      0.0027305478
Average Standardized Residual = 0.004677
Average Off-diagonal Standardized Residual = 0.006622
```
```           Rank Order of 5 Largest Variance Standardized Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y1,Y1     Y2,Y2
-0.0199    0.0107  0.006880 -0.002746  0.002731

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 78
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation

Distribution of Variance Standardized Residuals
(Each * represents 1 residuals)
```
```                    -0.02037 -   -0.01528  1  10.00% | *
-0.01528 -   -0.01018  0   0.00% |
-0.01018 -   -0.00509  0   0.00% |
-0.00509 -          0  2  20.00% | **
0 -    0.00509  5  50.00% | *****
0.00509 -    0.01018  1  10.00% | *
0.01018 -    0.01528  1  10.00% | *
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 79
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation

Manifest Variable Equations```
```                      X1      =    7.6010*F1 + 1.0000 E1
Z1

X2      =    7.6010*F1 + 1.0000 E2
Z1

Y1      =    8.5919*F2 + 1.0000 E3
Z3

Y2      =    8.5919*F2 + 1.0000 E4
Z3

```
```                      Variances of Exogenous Variables
-------------------------------------
Variable    Parameter      Estimate
-------------------------------------```
```                    F1                           1.000000
F2                           1.000000
E1          EPS1            28.555450
E2          EPS1            28.555450
E3          EPS3            23.732000
E4          EPS3            23.732000

```
```                     Covariances among Exogenous Variables
--------------------------------
Parameter          Estimate
--------------------------------```
```                       F2    F1    RO          0.898643
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 80
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation

Equations with Standardized Coefficients```
```                      X1      =    0.8181*F1 + 0.5751 E1
Z1

X2      =    0.8181*F1 + 0.5751 E2
Z1

Y1      =    0.8699*F2 + 0.4932 E3
Z3

Y2      =    0.8699*F2 + 0.4932 E4
Z3

```
```                         Squared Multiple Correlations
----------------------------------------------------------
Error           Total
Variable       Variance        Variance        R-squared
----------------------------------------------------------```
```             1    X1       28.555450       86.330550        0.669231
2    X2       28.555450       86.330550        0.669231
3    Y1       23.732000       97.552100        0.756725
4    Y2       23.732000       97.552100        0.756725

```
```                    Correlations among Exogenous Variables
--------------------------------
Parameter          Estimate
--------------------------------```
```                       F2    F1    RO          0.898643

```
```
Predicted Moments of Latent Variables
```
```                                      F1                F2

F1       1.000000000       0.898643396
F2       0.898643396       1.000000000```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 81
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```           Covariance Structure Analysis: Least-Squares Estimation

Predicted Moments between Manifest and Latent Variables
```
```                                      F1                F2

X1       7.600993356       6.830582482
X2       7.600993356       6.830582482
Y1       7.721020431       8.591862429
Y2       7.721020431       8.591862429
```
```
Latent Variable Score Regression Coefficients
```
```                                      F1                F2

X1      0.0362991938      0.0148461999
X2      0.0362991938      0.0148461999
Y1      0.0201923532      0.0399673456
Y2      0.0201923532      0.0399673456
```
```
Total Effects of Exogenous on Endogenous Variables
```
```                                      F1                F2

X1       7.600993356       0.000000000
X2       7.600993356       0.000000000
Y1       0.000000000       8.591862429
Y2       0.000000000       8.591862429
```
```
Indirect Effects of Exogenous on Endogenous Variables
```
```                                      F1                F2

X1                 0                 0
X2                 0                 0
Y1                 0                 0
Y2                 0                 0
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 82
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 5
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 0.003
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```Optimization Results: Iterations= 0 Function Calls= 2 Jacobian Calls= 1
Active Constraints= 0  Criterion= 0.0029838497
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                 83
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.33055000       57.77510000       58.68742500       58.68742500
X2       57.77510000       86.33055000       58.68742500       58.68742500
Y1       58.68742500       58.68742500       97.55210000       73.82010000
Y2       58.68742500       58.68742500       73.82010000       97.55210000
Determinant = 7399462 (Ln = 15.817)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 84
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0030
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9985
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9970
Root Mean Square Residual (RMR) . . . . . . . . .     0.6983
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.8321
Chi-square = 1.9335        df = 5       Prob>chi**2 = 0.8583
Null Model Chi-square:     df = 6                  1466.5524
RMSEA Estimate  . . . . . . . . . 0.0000  90%C.I.[., 0.0293]
Probability of Close Fit  . . . . . . . . . . . .     0.9936
ECVI Estimate . . . . . . . . . . 0.0185  90%C.I.[., 0.0276]
Bentler's Comparative Fit Index . . . . . . . . .     1.0000
Normal Theory Reweighted LS Chi-square  . . . . .     1.9568
Akaike's Information Criterion. . . . . . . . . .    -8.0665
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .   -35.4436
Schwarz's Bayesian Criterion. . . . . . . . . . .   -30.4436
McDonald's (1989) Centrality. . . . . . . . . . .     1.0024
Bentler & Bonett's (1980) Non-normed Index. . . .     1.0025
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9987
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.8322
Z-Test of Wilson & Hilferty (1931). . . . . . . .    -1.0768
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9984
Bollen (1988) Non-normed Index Delta2 . . . . . .     1.0021
Hoelter's (1983) Critical N . . . . . . . . . . .       3712

```
```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.067350000       0.000000000      -1.822325000       0.211175000
X2       0.000000000      -0.067350000       0.630275000       0.980875000
Y1      -1.822325000       0.630275000      -0.267100000       0.000000000
Y2       0.211175000       0.980875000       0.000000000       0.267100000
Average Absolute Residual = 0.4314
Average Off-diagonal Absolute Residual = 0.6074
```
```                      Rank Order of 5 Largest Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y2,Y2     Y1,Y1
-1.8223    0.9809    0.6303    0.2671   -0.2671

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 85
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Asymptotically Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1      0.0267263773      0.0000000000      -.9784404931      0.1133838207
X2      0.0000000000      -.0267263773      0.3384064762      0.5266501961
Y1      -.9784404931      0.3384064762      -.1066164052      0.0000000000
Y2      0.1133838207      0.5266501961      0.0000000000      0.1066164052
Average Standardized Residual = 0.2224
Average Off-diagonal Standardized Residual = 0.3261
```
```        Rank Order of 5 Largest Asymptotically Standardized Residuals
```
```                   Y1,X1     Y2,X2     Y1,X2     Y2,X1     Y2,Y2
-0.9784    0.5267    0.3384    0.1134    0.1066

```
```            Distribution of Asymptotically Standardized Residuals
(Each * represents 1 residuals)
```
```                    -1.00000 -   -0.75000  1  10.00% | *
-0.75000 -   -0.50000  0   0.00% |
-0.50000 -   -0.25000  0   0.00% |
-0.25000 -          0  2  20.00% | **
0 -    0.25000  5  50.00% | *****
0.25000 -    0.50000  1  10.00% | *
0.50000 -    0.75000  1  10.00% | *
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 86
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Manifest Variable Equations```
```                     X1      =     7.6010*F1 +  1.0000 E1
Std Err       0.2684 Z1
t Value      28.3158

X2      =     7.6010*F1 +  1.0000 E2
Std Err       0.2684 Z1
t Value      28.3158

Y1      =     8.5919*F2 +  1.0000 E3
Std Err       0.2797 Z3
t Value      30.7215

Y2      =     8.5919*F2 +  1.0000 E4
Std Err       0.2797 Z3
t Value      30.7215

```
```                      Variances of Exogenous Variables
---------------------------------------------------------------------
Standard
Variable    Parameter      Estimate          Error          t Value
---------------------------------------------------------------------```
```    F1                           1.000000               0           0.000
F2                           1.000000               0           0.000
E1          EPS1            28.555450        1.586414          18.000
E2          EPS1            28.555450        1.586414          18.000
E3          EPS3            23.732000        1.318444          18.000
E4          EPS3            23.732000        1.318444          18.000

```
```                    Covariances among Exogenous Variables
----------------------------------------------------------------
Standard
Parameter          Estimate          Error          t Value
----------------------------------------------------------------```
```       F2    F1    RO          0.898643        0.018652          48.180
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 87
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Equations with Standardized Coefficients```
```                      X1      =    0.8181*F1 + 0.5751 E1
Z1

X2      =    0.8181*F1 + 0.5751 E2
Z1

Y1      =    0.8699*F2 + 0.4932 E3
Z3

Y2      =    0.8699*F2 + 0.4932 E4
Z3

```
```                         Squared Multiple Correlations
----------------------------------------------------------
Error           Total
Variable       Variance        Variance        R-squared
----------------------------------------------------------```
```             1    X1       28.555450       86.330550        0.669231
2    X2       28.555450       86.330550        0.669231
3    Y1       23.732000       97.552100        0.756725
4    Y2       23.732000       97.552100        0.756725

```
```                    Correlations among Exogenous Variables
--------------------------------
Parameter          Estimate
--------------------------------```
```                       F2    F1    RO          0.898643

```
```
Predicted Moments of Latent Variables
```
```                                      F1                F2

F1       1.000000000       0.898643396
F2       0.898643396       1.000000000```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 88
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Moments between Manifest and Latent Variables
```
```                                      F1                F2

X1       7.600993356       6.830582482
X2       7.600993356       6.830582482
Y1       7.721020431       8.591862429
Y2       7.721020431       8.591862429
```
```
Latent Variable Score Regression Coefficients
```
```                                      F1                F2

X1      0.0362991938      0.0148461999
X2      0.0362991938      0.0148461999
Y1      0.0201923532      0.0399673456
Y2      0.0201923532      0.0399673456
```
```
Total Effects of Exogenous on Endogenous Variables
```
```                                      F1                F2

X1       7.600993356       0.000000000
X2       7.600993356       0.000000000
Y1       0.000000000       8.591862429
Y2       0.000000000       8.591862429
```
```
Indirect Effects of Exogenous on Endogenous Variables
```
```                                      F1                F2

X1                 0                 0
X2                 0                 0
Y1                 0                 0
Y2                 0                 0
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 89
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices _PHI_[6:6]
Symmetric Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                          F1                     F2                     E1

F1            SING               2321.323 [RO  ]           0.488
.      .                                     0.485  0.154

F2        2321.323 [RO  ]            SING                  0.831
.      .              0.362 -0.194

E1           0.488                  0.831                324.000 [EPS1]
0.485  0.154           0.362 -0.194

E2           0.488                  0.831                   SING
0.485 -0.154           0.362  0.194            .      .

E3           0.436                  0.179                  1.789
0.509 -0.133           0.673  0.082           0.181 -2.061

E4           0.436                  0.179                  0.323
0.509  0.133           0.673 -0.082           0.570  0.876

E2                     E3                     E4

F1           0.488                  0.436                  0.436
0.485 -0.154           0.509 -0.133           0.509  0.133

F2           0.831                  0.179                  0.179
0.362  0.194           0.673  0.082           0.673 -0.082

E1            SING                  1.789                  0.323
.      .              0.181 -2.061           0.570  0.876

E2         324.000 [EPS1]           0.451                  0.010
0.502  1.034           0.922  0.151

E3           0.451                324.000 [EPS3]            SING
0.502  1.034                                   .      .

E4           0.010                   SING                324.000 [EPS3]
0.922  0.151            .      .```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 90
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Rank order of 10 largest Lagrange multipliers in _PHI_
```
```                 E3 : E1             E1 : F2             E2 : F2
1.7894 : 0.181      0.8313 : 0.362      0.8313 : 0.362

E1 : F1             E2 : F1             E3 : E2
0.4883 : 0.485      0.4883 : 0.485      0.4505 : 0.502

E3 : F1             E4 : F1             E4 : E1
0.4364 : 0.509      0.4364 : 0.509      0.3235 : 0.570

E3 : F2
0.1785 : 0.673

```
```            Lagrange Multiplier and Wald Test Indices _GAMMA_[4:2]
General Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                      F1                    F2

X1        801.785   [Z1]          0.205
0.651 -0.143

X2        801.785   [Z1]          0.205
0.651  0.143

Y1          0.150               943.808   [Z3]
0.699 -0.113

Y2          0.150               943.808   [Z3]
0.699  0.113
```
```           Rank order of 4 largest Lagrange multipliers in _GAMMA_
```
```                 X1 : F2             X2 : F2             Y1 : F1
0.2050 : 0.651      0.2050 : 0.651      0.1497 : 0.699

Y2 : F1
0.1497 : 0.699

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 91
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 2, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Univariate Lagrange Multiplier Test
For Releasing Equality Constraints
------------------------------------------------------------
Chi-Square    Prob          Change       Parameter Equal to
------------------------------------------------------------```
```             0.047575   0.8273  -0.0348 =   0.0348  [X1:F1] = [X2:F1]
0.049417   0.8241  -0.0319 =   0.0319  [Y1:F2] = [Y2:F2]
0.488258   0.4847   1.1708 =  -1.1708  [E1:E1] = [E2:E2]
0.178518   0.6726   0.7038 =  -0.7038  [E3:E3] = [E4:E4]

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 92
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

FACTOR Model Statement
-------------------------------
Matrix         Rows & Cols          Matrix Type```
``` TERM   1-----------------------------------------------------------
1    _F_            4       2    GENERAL
2    _P_            2       2    SYMMETRIC
TERM   2-----------------------------------------------------------
3    _U_            4       4    SYMMETRIC

```
```                      Initial Parameter Matrix _P_[2:2]
Symmetric Matrix
Constant Model Matrix```
```                                    FCOR1       FCOR2

FCOR1        1.00        1.00
FCOR2        1.00        1.00
```
```                      Initial Parameter Matrix _F_[4:2]
Lower Triangular Matrix```
```                                   FACT1           FACT2

X1         .  [Z1]          .0
X2         .  [Z2]          .0
Y1          .0             .  [Z3]
Y2          .0             .  [Z4]
```
```                      Initial Parameter Matrix _U_[4:4]
Diagonal Matrix```
```                 UVAR1             UVAR2             UVAR3             UVAR4

X1         .  [EPS1]          .0                .0                .0
X2          .0               .  [EPS2]          .0                .0
Y1          .0                .0               .  [EPS3]          .0
Y2          .0                .0                .0               .  [EPS4]```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 93
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          2
4 Variables          Model Matrices       3
10 Informations       Parameters           8

VARIABLE              Mean           Std Dev

X1                       0       9.295047068
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942
```
```
Covariances
```
```                    X1                X2                Y1                Y2

X1       86.39790000       57.77510000       56.86510000       58.89860000
X2       57.77510000       86.26320000       59.31770000       59.66830000
Y1       56.86510000       59.31770000       97.28500000       73.82010000
Y2       58.89860000       59.66830000       73.82010000       97.81920000
Determinant = 7377416 (Ln = 15.814)

Some initial estimates computed by McDonald's method.

```
```                         Vector of Initial Estimates
```
```             Z1            1    8.49170  Matrix Entry: _F_[1:1]
Z2            2    8.48508  Matrix Entry: _F_[2:1]
Z3            3    9.24400  Matrix Entry: _F_[3:2]
Z4            4    9.26935  Matrix Entry: _F_[4:2]
EPS1          5   14.28885  Matrix Entry: _U_[1:1]
EPS2          6   14.26658  Matrix Entry: _U_[2:2]
EPS3          7   11.83337  Matrix Entry: _U_[3:3]
EPS4          8   11.89835  Matrix Entry: _U_[4:4]

```
```
Predetermined Elements of the Predicted Moment Matrix
```
```                    X1                X2                Y1                Y2

X1                 .                 .                 .                 .
X2                 .                 .                 .                 .
Y1                 .                 .                 .                 .
Y2                 .                 .                 .                 .
Sum of Squared Differences = 0```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 94
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 8
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 1.541
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    2   0    0.2751   1.2662  0.0219   1.345   0.636
2    0    4   0    0.0563   0.2188 0.00257       0   0.808
3    0    5   0    0.0559 0.000423 0.00034       0   1.207
4    0    6   0    0.0559  0.00003 0.00009       0   1.301
5    0    7   0    0.0559 2.806E-6 0.00003       0   1.303
6    0    8   0    0.0559  2.63E-7 8.27E-6       0   1.304

Optimization Results: Iterations= 6 Function Calls= 9 Jacobian Calls= 7
Active Constraints= 0  Criterion= 0.055878809
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                 95
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.39790092       51.64564678       59.49111336       60.46546987
X2       51.64564678       86.26320075       60.86742432       61.86432230
Y1       59.49111336       60.86742432       97.28500041       71.26210322
Y2       60.46546987       61.86432230       71.26210322       97.81920061
Determinant = 7801393 (Ln = 15.870)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 96
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0559
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9714
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.8570
Root Mean Square Residual (RMR) . . . . . . . . .     2.4635
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.3238
Chi-square = 36.2095       df = 2       Prob>chi**2 = 0.0001
Null Model Chi-square:     df = 6                  1466.5524
RMSEA Estimate  . . . . . .  0.1625  90%C.I.[0.1187, 0.2108]
Probability of Close Fit  . . . . . . . . . . . .     0.0000
ECVI Estimate . . . . . . .  0.0808  90%C.I.[0.0561, 0.1170]
Bentler's Comparative Fit Index . . . . . . . . .     0.9766
Normal Theory Reweighted LS Chi-square  . . . . .    38.1439
Akaike's Information Criterion. . . . . . . . . .    32.2095
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .    21.2586
Schwarz's Bayesian Criterion. . . . . . . . . . .    23.2586
McDonald's (1989) Centrality. . . . . . . . . . .     0.9740
Bentler & Bonett's (1980) Non-normed Index. . . .     0.9297
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9753
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.3251
Z-Test of Wilson & Hilferty (1931). . . . . . . .     5.2108
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9259
Bollen (1988) Non-normed Index Delta2 . . . . . .     0.9766
Hoelter's (1983) Critical N . . . . . . . . . . .        109

```
```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1      -0.000000916       6.129453223      -2.626013365      -1.566869871
X2       6.129453223       0.000000000      -1.549724320      -2.196022303
Y1      -2.626013365      -1.549724320       0.000000000       2.557996783
Y2      -1.566869871      -2.196022303       2.557996783       0.000000000
Average Absolute Residual = 1.663
Average Off-diagonal Absolute Residual = 2.771
```
```                      Rank Order of 5 Largest Residuals
```
```                   X2,X1     Y1,X1     Y2,Y1     Y2,X2     Y2,X1
6.1295   -2.6260    2.5580   -2.1960   -1.5669

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 97
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Asymptotically Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.000000000       6.129683715      -3.565481795      -2.310841084
X2       6.129683715       0.000000000      -2.310555458      -3.566058039
Y1      -3.565481795      -2.310555458       0.000000000       6.142554074
Y2      -2.310841084      -3.566058039       6.142554074       0.000000000
Average Standardized Residual = 2.403
Average Off-diagonal Standardized Residual = 4.004
```
```        Rank Order of 5 Largest Asymptotically Standardized Residuals
```
```                   Y2,Y1     X2,X1     Y2,X2     Y1,X1     Y2,X1
6.1426    6.1297   -3.5661   -3.5655   -2.3108

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 98
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Distribution of Asymptotically Standardized Residuals
(Each * represents 1 residuals)
```
```                    -3.75000 -   -3.50000  2  20.00% | **
-3.50000 -   -3.25000  0   0.00% |
-3.25000 -   -3.00000  0   0.00% |
-3.00000 -   -2.75000  0   0.00% |
-2.75000 -   -2.50000  0   0.00% |
-2.50000 -   -2.25000  2  20.00% | **
-2.25000 -   -2.00000  0   0.00% |
-2.00000 -   -1.75000  0   0.00% |
-1.75000 -   -1.50000  0   0.00% |
-1.50000 -   -1.25000  0   0.00% |
-1.25000 -   -1.00000  0   0.00% |
-1.00000 -   -0.75000  0   0.00% |
-0.75000 -   -0.50000  0   0.00% |
-0.50000 -   -0.25000  0   0.00% |
-0.25000 -          0  0   0.00% |
0 -    0.25000  4  40.00% | ****
0.25000 -    0.50000  0   0.00% |
0.50000 -    0.75000  0   0.00% |
0.75000 -    1.00000  0   0.00% |
1.00000 -    1.25000  0   0.00% |
1.25000 -    1.50000  0   0.00% |
1.50000 -    1.75000  0   0.00% |
1.75000 -    2.00000  0   0.00% |
2.00000 -    2.25000  0   0.00% |
2.25000 -    2.50000  0   0.00% |
2.50000 -    2.75000  0   0.00% |
2.75000 -    3.00000  0   0.00% |
3.00000 -    3.25000  0   0.00% |
3.25000 -    3.50000  0   0.00% |
3.50000 -    3.75000  0   0.00% |
3.75000 -    4.00000  0   0.00% |
4.00000 -    4.25000  0   0.00% |
4.25000 -    4.50000  0   0.00% |
4.50000 -    4.75000  0   0.00% |
4.75000 -    5.00000  0   0.00% |
5.00000 -    5.25000  0   0.00% |
5.25000 -    5.50000  0   0.00% |
5.50000 -    5.75000  0   0.00% |
5.75000 -    6.00000  0   0.00% |
6.00000 -    6.25000  2  20.00% | **
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                 99
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix _P_[2:2]
Symmetric Matrix
Constant Model Matrix```
```                     *** Constant or Unchanged Matrix ***

```
```                     Estimated Parameter Matrix _F_[4:2]
Standard Errors and t Values
Lower Triangular Matrix```
```                                   FACT1                  FACT2

X1        7.1048     [Z1]        0.
0.3218  22.0804        0.       0.

X2        7.2691     [Z2]        0.
0.3183  22.8400        0.       0.

Y1        0.                     8.3734     [Z3]
0.       0.            0.3254  25.7312

Y2        0.                     8.5105     [Z4]
0.       0.            0.3241  26.2597
```
```                     Estimated Parameter Matrix _U_[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                   UVAR1                   UVAR2

X1        35.9200   [EPS1]         0.
2.4146  14.8760         0.       0.

X2         0.                     33.4227   [EPS2]
0.       0.             2.3103  14.4666

Y1         0.                      0.
0.       0.             0.       0.

Y2         0.                      0.
0.       0.             0.       0.```

```                  TEST32: Vocabulary Test Data, LORD (1957)                100
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix _U_[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                   UVAR3                   UVAR4

X1         0.                      0.
0.       0.             0.       0.

X2         0.                      0.
0.       0.             0.       0.

Y1        27.1712   [EPS3]         0.
2.2462  12.0963         0.       0.

Y2         0.                     25.3900   [EPS4]
0.       0.             2.2084  11.4970```

```                  TEST32: Vocabulary Test Data, LORD (1957)                101
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

```
```                                   FACT1             FACT2

X1      0.7643615824      0.0000000000
X2      0.7826552269      0.0000000000
Y1      0.0000000000      0.8489433441
Y2      0.0000000000      0.8604882233
```
```                        Squared Multiple Correlations
-------------------------------------------------------------
Error           Total
Parameter        Variance        Variance        R-squared
-------------------------------------------------------------```
```           1    X1          35.920046       86.397901        0.584249
2    X2          33.422746       86.263201        0.612549
3    Y1          27.171233       97.285000        0.720705
4    Y2          25.389953       97.819201        0.740440

```
```                    Correlations among Exogenous Variables
------------------------------------------------------
Row & Column          Parameter             Estimate
------------------------------------------------------```
```               2       1    FCOR2    FCOR1                1.000000

```
```
Factor Score Regression Coefficients
```
```                                   FACT1             FACT2

X1      0.0029801059      0.0029801059
X2      0.0032951318      0.0032951318
Y1      0.0027329576      0.0027329576
Y2      0.0028796731      0.0028796731
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                102
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices _P_[2:2]
Symmetric Matrix
Constant Model Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                    FCOR1                FCOR2

FCOR1        37.623               37.631
0.000  0.220         0.000 -0.110

FCOR2        37.631               37.640
0.000 -0.110         0.000  0.220
```
```             Rank order of 3 largest Lagrange multipliers in _P_
```
```              FCOR2 : FCOR2       FCOR2 : FCOR1       FCOR1 : FCOR1
37.6398 : 0.000     37.6314 : 0.000     37.6230 : 0.000

```
```              Lagrange Multiplier and Wald Test Indices _F_[4:2]
Lower Triangular Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                   FACT1                 FACT2

X1        487.545   [Z1]           SING
.      .

X2        521.666   [Z2]           SING
.      .

Y1           SING               662.094   [Z3]
.      .

Y2           SING               689.572   [Z4]
.      .```

```                  TEST32: Vocabulary Test Data, LORD (1957)                103
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices _U_[4:4]
Diagonal Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                UVAR1              UVAR2              UVAR3              UVAR4

X1    221.295  [EPS1]     37.598             12.708              5.336
0.000  11.364      0.000  -7.290      0.021  -4.794

X2     37.598            209.283  [EPS2]      5.336             12.710
0.000  11.364                         0.021  -4.826      0.000  -7.580

Y1     12.708              5.336            146.321  [EPS3]     37.685
0.000  -7.290      0.021  -4.826                         0.000  15.681

Y2      5.336             12.710             37.685            132.180  [EPS4]
0.021  -4.794      0.000  -7.580      0.000  15.681
```
```             Rank order of 6 largest Lagrange multipliers in _U_
```
```                 Y2 : UVAR3          X2 : UVAR1          Y2 : UVAR2
37.6852 : 0.000     37.5980 : 0.000     12.7100 : 0.000

Y1 : UVAR1          Y1 : UVAR2          Y2 : UVAR1
12.7079 : 0.000      5.3358 : 0.021      5.3355 : 0.021

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                104
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

COSAN Model Statement
-------------------------------
Matrix         Rows & Cols          Matrix Type```
``` TERM   1-----------------------------------------------------------
1    F              4       2    GENERAL
2    PHI            2       2    SYMMETRIC
TERM   2-----------------------------------------------------------
3    U              4       4    DIAGONAL

```
```                      Initial Parameter Matrix PHI[2:2]
Symmetric Matrix
Constant Model Matrix```
```                                     COL1        COL2

ROW1        1.00        1.00
ROW2        1.00        1.00
```
```                       Initial Parameter Matrix F[4:2]
Lower Triangular Matrix```
```                                    COL1            COL2

X1         .  [Z1]          .0
X2         .  [Z2]          .0
Y1          .0             .  [Z3]
Y2          .0             .  [Z4]
```
```                       Initial Parameter Matrix U[4:4]
Diagonal Matrix```
```                  COL1              COL2              COL3              COL4

X1         .  [EPS1]          .0                .0                .0
X2          .0               .  [EPS2]          .0                .0
Y1          .0                .0               .  [EPS3]          .0
Y2          .0                .0                .0               .  [EPS4]```

```                  TEST32: Vocabulary Test Data, LORD (1957)                105
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          2
4 Variables          Model Matrices       3
10 Informations       Parameters           8

VARIABLE              Mean           Std Dev

X1                       0       9.295047068
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942
```
```
Covariances
```
```                    X1                X2                Y1                Y2

X1       86.39790000       57.77510000       56.86510000       58.89860000
X2       57.77510000       86.26320000       59.31770000       59.66830000
Y1       56.86510000       59.31770000       97.28500000       73.82010000
Y2       58.89860000       59.66830000       73.82010000       97.81920000
Determinant = 7377416 (Ln = 15.814)

```
```                         Vector of Initial Estimates
```
```             Z1            1    0.50000  Matrix Entry: F[1:1]
Z2            2    0.50000  Matrix Entry: F[2:1]
Z3            3    0.50000  Matrix Entry: F[3:2]
Z4            4    0.50000  Matrix Entry: F[4:2]
EPS1          5   50.00000  Matrix Entry: U[1:1]
EPS2          6   50.00000  Matrix Entry: U[2:2]
EPS3          7   50.00000  Matrix Entry: U[3:3]
EPS4          8   50.00000  Matrix Entry: U[4:4]

```
```
Predetermined Elements of the Predicted Moment Matrix
```
```                    X1                X2                Y1                Y2

X1                 .                 .                 .                 .
X2                 .                 .                 .                 .
Y1                 .                 .                 .                 .
Y2                 .                 .                 .                 .
Sum of Squared Differences = 0```

```                  TEST32: Vocabulary Test Data, LORD (1957)                106
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 8
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 3.101
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    2   0    1.1441   1.9573  0.0248   3.919   0.402
2    0    3   0    0.5524   0.5917  0.0258   0.240   1.333
3    0    4   0    0.0964   0.4560  0.0134       0   1.665
4    0    5   0    0.0563   0.0401 0.00219       0   1.206
5    0    6   0    0.0559 0.000391  0.0002       0   1.085
6    0    7   0    0.0559 0.000011 0.00005       0   1.306
7    0    8   0    0.0559 1.001E-6 0.00002       0   1.306
8    0    9   0    0.0559 9.393E-8 5.01E-6       0   1.306

Optimization Results: Iterations= 8 Function Calls= 10 Jacobian Calls= 9
Active Constraints= 0  Criterion= 0.055878792
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                107
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.39790030       51.64333255       59.49079992       60.46494639
X2       51.64333255       86.26320029       60.86705346       61.86373572
Y1       59.49079992       60.86705346       97.28500019       71.26424540
Y2       60.46494639       61.86373572       71.26424540       97.81920017
Determinant = 7801392 (Ln = 15.870)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                108
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0559
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9714
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.8571
Root Mean Square Residual (RMR) . . . . . . . . .     2.4637
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.3238
Chi-square = 36.2095       df = 2       Prob>chi**2 = 0.0001
Null Model Chi-square:     df = 6                  1466.5524
RMSEA Estimate  . . . . . .  0.1625  90%C.I.[0.1187, 0.2108]
Probability of Close Fit  . . . . . . . . . . . .     0.0000
ECVI Estimate . . . . . . .  0.0808  90%C.I.[0.0561, 0.1170]
Bentler's Comparative Fit Index . . . . . . . . .     0.9766
Normal Theory Reweighted LS Chi-square  . . . . .    38.1423
Akaike's Information Criterion. . . . . . . . . .    32.2095
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .    21.2586
Schwarz's Bayesian Criterion. . . . . . . . . . .    23.2586
McDonald's (1989) Centrality. . . . . . . . . . .     0.9740
Bentler & Bonett's (1980) Non-normed Index. . . .     0.9297
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9753
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.3251
Z-Test of Wilson & Hilferty (1931). . . . . . . .     5.2108
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9259
Bollen (1988) Non-normed Index Delta2 . . . . . .     0.9766
Hoelter's (1983) Critical N . . . . . . . . . . .        109

```
```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.000000000       6.131767451      -2.625699920      -1.566346385
X2       6.131767451       0.000000000      -1.549353456      -2.195435717
Y1      -2.625699920      -1.549353456       0.000000000       2.555854604
Y2      -1.566346385      -2.195435717       2.555854604       0.000000000
Average Absolute Residual = 1.662
Average Off-diagonal Absolute Residual = 2.771
```
```                      Rank Order of 5 Largest Residuals
```
```                   X2,X1     Y1,X1     Y2,Y1     Y2,X2     Y2,X1
6.1318   -2.6257    2.5559   -2.1954   -1.5663

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                109
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Asymptotically Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.000000000       6.131160645      -3.565158155      -2.310104703
X2       6.131160645       0.000000000      -2.310043838      -3.565119127
Y1      -3.565158155      -2.310043838       0.000000000       6.138850383
Y2      -2.310104703      -3.565119127       6.138850383       0.000000000
Average Standardized Residual = 2.402
Average Off-diagonal Standardized Residual = 4.003
```
```        Rank Order of 5 Largest Asymptotically Standardized Residuals
```
```                   Y2,Y1     X2,X1     Y1,X1     Y2,X2     Y2,X1
6.1389    6.1312   -3.5652   -3.5651   -2.3101

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                110
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Distribution of Asymptotically Standardized Residuals
(Each * represents 1 residuals)
```
```                    -3.75000 -   -3.50000  2  20.00% | **
-3.50000 -   -3.25000  0   0.00% |
-3.25000 -   -3.00000  0   0.00% |
-3.00000 -   -2.75000  0   0.00% |
-2.75000 -   -2.50000  0   0.00% |
-2.50000 -   -2.25000  2  20.00% | **
-2.25000 -   -2.00000  0   0.00% |
-2.00000 -   -1.75000  0   0.00% |
-1.75000 -   -1.50000  0   0.00% |
-1.50000 -   -1.25000  0   0.00% |
-1.25000 -   -1.00000  0   0.00% |
-1.00000 -   -0.75000  0   0.00% |
-0.75000 -   -0.50000  0   0.00% |
-0.50000 -   -0.25000  0   0.00% |
-0.25000 -          0  0   0.00% |
0 -    0.25000  4  40.00% | ****
0.25000 -    0.50000  0   0.00% |
0.50000 -    0.75000  0   0.00% |
0.75000 -    1.00000  0   0.00% |
1.00000 -    1.25000  0   0.00% |
1.25000 -    1.50000  0   0.00% |
1.50000 -    1.75000  0   0.00% |
1.75000 -    2.00000  0   0.00% |
2.00000 -    2.25000  0   0.00% |
2.25000 -    2.50000  0   0.00% |
2.50000 -    2.75000  0   0.00% |
2.75000 -    3.00000  0   0.00% |
3.00000 -    3.25000  0   0.00% |
3.25000 -    3.50000  0   0.00% |
3.50000 -    3.75000  0   0.00% |
3.75000 -    4.00000  0   0.00% |
4.00000 -    4.25000  0   0.00% |
4.25000 -    4.50000  0   0.00% |
4.50000 -    4.75000  0   0.00% |
4.75000 -    5.00000  0   0.00% |
5.00000 -    5.25000  0   0.00% |
5.25000 -    5.50000  0   0.00% |
5.50000 -    5.75000  0   0.00% |
5.75000 -    6.00000  0   0.00% |
6.00000 -    6.25000  2  20.00% | **
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                111
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix PHI[2:2]
Symmetric Matrix
Constant Model Matrix```
```                     *** Constant or Unchanged Matrix ***

```
```                      Estimated Parameter Matrix F[4:2]
Standard Errors and t Values
Lower Triangular Matrix```
```                                    COL1                   COL2

X1        7.1046     [Z1]        0.
0.3218  22.0798        0.       0.

X2        7.2690     [Z2]        0.
0.3183  22.8393        0.       0.

Y1        0.                     8.3735     [Z3]
0.       0.            0.3254  25.7319

Y2        0.                     8.5107     [Z4]
0.       0.            0.3241  26.2603
```
```                      Estimated Parameter Matrix U[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                    COL1                    COL2

X1        35.9223   [EPS1]         0.
2.4147  14.8764         0.       0.

X2         0.                     33.4252   [EPS2]
0.       0.             2.3104  14.4672

Y1         0.                      0.
0.       0.             0.       0.

Y2         0.                      0.
0.       0.             0.       0.```

```                  TEST32: Vocabulary Test Data, LORD (1957)                112
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Estimated Parameter Matrix U[4:4]
Standard Errors and t Values
Diagonal Matrix```
```                                    COL3                    COL4

X1         0.                      0.
0.       0.             0.       0.

X2         0.                      0.
0.       0.             0.       0.

Y1        27.1689   [EPS3]         0.
2.2462  12.0957         0.       0.

Y2         0.                     25.3880   [EPS4]
0.       0.             2.2083  11.4964```

```                  TEST32: Vocabulary Test Data, LORD (1957)                113
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices PHI[2:2]
Symmetric Matrix
Constant Model Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                     COL1                 COL2

ROW1        37.621               37.626
0.000  0.220         0.000 -0.110

ROW2        37.626               37.631
0.000 -0.110         0.000  0.220
```
```             Rank order of 3 largest Lagrange multipliers in PHI
```
```               ROW2 : COL2         ROW2 : COL1         ROW1 : COL1
37.6310 : 0.000     37.6260 : 0.000     37.6210 : 0.000

```
```               Lagrange Multiplier and Wald Test Indices F[4:2]
Lower Triangular Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                    COL1                  COL2

X1        487.517   [Z1]           SING
.      .

X2        521.634   [Z2]           SING
.      .

Y1           SING               662.129   [Z3]
.      .

Y2           SING               689.602   [Z4]
.      .```

```                  TEST32: Vocabulary Test Data, LORD (1957)                114
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices U[4:4]
Diagonal Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                 COL1               COL2               COL3               COL4

X1    221.308  [EPS1]     37.606             12.707              5.334
0.000  11.364      0.000  -7.289      0.021  -4.794

X2     37.606            209.299  [EPS2]      5.335             12.707
0.000  11.364                         0.021  -4.825      0.000  -7.580

Y1     12.707              5.335            146.307  [EPS3]     37.658
0.000  -7.289      0.021  -4.825                         0.000  15.682

Y2      5.334             12.707             37.658            132.168  [EPS4]
0.021  -4.794      0.000  -7.580      0.000  15.682
```
```              Rank order of 6 largest Lagrange multipliers in U
```
```                 Y2 : COL3           X2 : COL1           Y1 : COL1
37.6583 : 0.000     37.6061 : 0.000     12.7070 : 0.000

Y2 : COL2           Y1 : COL2           Y2 : COL1
12.7066 : 0.000      5.3346 : 0.021      5.3339 : 0.021

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                115
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

LINEQS Model Statement
-------------------------------
Matrix         Rows & Cols          Matrix Type```
``` TERM   1-----------------------------------------------------------
1    _SEL_          4      10    SELECTION
2    _BETA_        10      10    EQSBETA        IMINUSINV
3    _GAMMA_       10       6    EQSGAMMA
4    _PHI_          6       6    SYMMETRIC

```
```     Number of endogenous variables = 4
```
```Manifest:     X1        X2        Y1        Y2

```
```     Number of exogenous variables = 6
```
```Latent:       F1        F2
Error:        E1        E2        E3        E4
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                116
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```          Covariance Structure Analysis: Pattern and Initial Values

Manifest Variable Equations
Initial Estimates```
```                      X1      =     .    *F1 + 1.0000 E1
Z1

X2      =     .    *F1 + 1.0000 E2
Z2

Y1      =     .    *F2 + 1.0000 E3
Z3

Y2      =     .    *F2 + 1.0000 E4
Z4

```
```                      Variances of Exogenous Variables
-------------------------------------
Variable    Parameter      Estimate
-------------------------------------```
```                    F1                           1.000000
F2                           1.000000
E1          EPS1                    .
E2          EPS2                    .
E3          EPS3                    .
E4          EPS4                    .

```
```                     Covariances among Exogenous Variables
--------------------------------
Parameter          Estimate
--------------------------------```
```                       F2    F1                1.000000
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                117
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          1
4 Variables          Model Matrices       4
10 Informations       Parameters           8

VARIABLE              Mean           Std Dev

X1                       0       9.295047068
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942
```
```
Covariances
```
```                    X1                X2                Y1                Y2

X1       86.39790000       57.77510000       56.86510000       58.89860000
X2       57.77510000       86.26320000       59.31770000       59.66830000
Y1       56.86510000       59.31770000       97.28500000       73.82010000
Y2       58.89860000       59.66830000       73.82010000       97.81920000
Determinant = 7377416 (Ln = 15.814)

Some initial estimates computed by instrumental variable method.

```
```                         Vector of Initial Estimates
```
```           Z1            1    7.55181  Matrix Entry: _GAMMA_[1:1]
Z2            2    7.65050  Matrix Entry: _GAMMA_[2:1]
Z3            3    8.56658  Matrix Entry: _GAMMA_[3:2]
Z4            4    8.61722  Matrix Entry: _GAMMA_[4:2]
EPS1          5   29.36808  Matrix Entry: _PHI_[3:3]
EPS2          6   27.73308  Matrix Entry: _PHI_[4:4]
EPS3          7   23.89865  Matrix Entry: _PHI_[5:5]
EPS4          8   23.56278  Matrix Entry: _PHI_[6:6]

```
```
Predetermined Elements of the Predicted Moment Matrix
```
```                    X1                X2                Y1                Y2

X1                 .                 .                 .                 .
X2                 .                 .                 .                 .
Y1                 .                 .                 .                 .
Y2                 .                 .                 .                 .
Sum of Squared Differences = 0```

```                  TEST32: Vocabulary Test Data, LORD (1957)                118
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 8
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 0.097
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    2   0    0.0561   0.0407 0.00112       0   0.906
2    0    3   0    0.0559 0.000224 0.00028       0   1.257
3    0    4   0    0.0559 0.000021 0.00008       0   1.281
4    0    5   0    0.0559  1.92E-6 0.00002       0   1.292
5    0    6   0    0.0559 1.789E-7 6.96E-6       0   1.298

Optimization Results: Iterations= 5 Function Calls= 7 Jacobian Calls= 6
Active Constraints= 0  Criterion= 0.055878801
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```                  TEST32: Vocabulary Test Data, LORD (1957)                119
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
```
```                    X1                X2                Y1                Y2

X1       86.39790065       51.64461738       59.49082580       60.46528318
X2       51.64461738       86.26320048       60.86720481       61.86420722
Y1       59.49082580       60.86720481       97.28500023       71.26304660
Y2       60.46528318       61.86420722       71.26304660       97.81920048
Determinant = 7801393 (Ln = 15.870)```

```                  TEST32: Vocabulary Test Data, LORD (1957)                120
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0559
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9714
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.8570
Root Mean Square Residual (RMR) . . . . . . . . .     2.4636
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.3238
Chi-square = 36.2095       df = 2       Prob>chi**2 = 0.0001
Null Model Chi-square:     df = 6                  1466.5524
RMSEA Estimate  . . . . . .  0.1625  90%C.I.[0.1187, 0.2108]
Probability of Close Fit  . . . . . . . . . . . .     0.0000
ECVI Estimate . . . . . . .  0.0808  90%C.I.[0.0561, 0.1170]
Bentler's Comparative Fit Index . . . . . . . . .     0.9766
Normal Theory Reweighted LS Chi-square  . . . . .    38.1432
Akaike's Information Criterion. . . . . . . . . .    32.2095
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .    21.2586
Schwarz's Bayesian Criterion. . . . . . . . . . .    23.2586
McDonald's (1989) Centrality. . . . . . . . . . .     0.9740
Bentler & Bonett's (1980) Non-normed Index. . . .     0.9297
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9753
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.3251
Z-Test of Wilson & Hilferty (1931). . . . . . . .     5.2108
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9259
Bollen (1988) Non-normed Index Delta2 . . . . . .     0.9766
Hoelter's (1983) Critical N . . . . . . . . . . .        109
```
`WARNING: The central parameter matrix _PHI_ has probably 1 zero eigenvalue(s).`

```
Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.000000000       6.130482617      -2.625725802      -1.566683177
X2       6.130482617       0.000000000      -1.549504812      -2.195907220
Y1      -2.625725802      -1.549504812       0.000000000       2.557053402
Y2      -1.566683177      -2.195907220       2.557053402       0.000000000
Average Absolute Residual = 1.663
Average Off-diagonal Absolute Residual = 2.771
```
```                      Rank Order of 5 Largest Residuals
```
```                   X2,X1     Y1,X1     Y2,Y1     Y2,X2     Y2,X1
6.1305   -2.6257    2.5571   -2.1959   -1.5667

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                121
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Asymptotically Standardized Residual Matrix
```
```                    X1                X2                Y1                Y2

X1       0.000000000       6.130342711      -3.565090493      -2.310598968
X2       6.130342711       0.000000000      -2.310230342      -3.565928158
Y1      -3.565090493      -2.310230342       0.000000000       6.140930096
Y2      -2.310598968      -3.565928158       6.140930096       0.000000000
Average Standardized Residual = 2.402
Average Off-diagonal Standardized Residual = 4.004
```
```        Rank Order of 5 Largest Asymptotically Standardized Residuals
```
```                   Y2,Y1     X2,X1     Y2,X2     Y1,X1     Y2,X1
6.1409    6.1303   -3.5659   -3.5651   -2.3106

```

```                  TEST32: Vocabulary Test Data, LORD (1957)                122
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Distribution of Asymptotically Standardized Residuals
(Each * represents 1 residuals)
```
```                    -3.75000 -   -3.50000  2  20.00% | **
-3.50000 -   -3.25000  0   0.00% |
-3.25000 -   -3.00000  0   0.00% |
-3.00000 -   -2.75000  0   0.00% |
-2.75000 -   -2.50000  0   0.00% |
-2.50000 -   -2.25000  2  20.00% | **
-2.25000 -   -2.00000  0   0.00% |
-2.00000 -   -1.75000  0   0.00% |
-1.75000 -   -1.50000  0   0.00% |
-1.50000 -   -1.25000  0   0.00% |
-1.25000 -   -1.00000  0   0.00% |
-1.00000 -   -0.75000  0   0.00% |
-0.75000 -   -0.50000  0   0.00% |
-0.50000 -   -0.25000  0   0.00% |
-0.25000 -          0  0   0.00% |
0 -    0.25000  4  40.00% | ****
0.25000 -    0.50000  0   0.00% |
0.50000 -    0.75000  0   0.00% |
0.75000 -    1.00000  0   0.00% |
1.00000 -    1.25000  0   0.00% |
1.25000 -    1.50000  0   0.00% |
1.50000 -    1.75000  0   0.00% |
1.75000 -    2.00000  0   0.00% |
2.00000 -    2.25000  0   0.00% |
2.25000 -    2.50000  0   0.00% |
2.50000 -    2.75000  0   0.00% |
2.75000 -    3.00000  0   0.00% |
3.00000 -    3.25000  0   0.00% |
3.25000 -    3.50000  0   0.00% |
3.50000 -    3.75000  0   0.00% |
3.75000 -    4.00000  0   0.00% |
4.00000 -    4.25000  0   0.00% |
4.25000 -    4.50000  0   0.00% |
4.50000 -    4.75000  0   0.00% |
4.75000 -    5.00000  0   0.00% |
5.00000 -    5.25000  0   0.00% |
5.25000 -    5.50000  0   0.00% |
5.50000 -    5.75000  0   0.00% |
5.75000 -    6.00000  0   0.00% |
6.00000 -    6.25000  2  20.00% | **
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                123
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Manifest Variable Equations```
```                     X1      =     7.1047*F1 +  1.0000 E1
Std Err       0.3218 Z1
t Value      22.0801

X2      =     7.2691*F1 +  1.0000 E2
Std Err       0.3183 Z2
t Value      22.8397

Y1      =     8.3734*F2 +  1.0000 E3
Std Err       0.3254 Z3
t Value      25.7314

Y2      =     8.5106*F2 +  1.0000 E4
Std Err       0.3241 Z4
t Value      26.2600

```
```                      Variances of Exogenous Variables
---------------------------------------------------------------------
Standard
Variable    Parameter      Estimate          Error          t Value
---------------------------------------------------------------------```
```    F1                           1.000000               0           0.000
F2                           1.000000               0           0.000
E1          EPS1            35.921114        2.414672          14.876
E2          EPS2            33.423734        2.310368          14.467
E3          EPS3            27.170428        2.246207          12.096
E4          EPS4            25.388868        2.208372          11.497

```
```                    Covariances among Exogenous Variables
----------------------------------------------------------------
Standard
Parameter          Estimate          Error          t Value
----------------------------------------------------------------```
```       F2    F1                1.000000               0           0.000
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                124
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Equations with Standardized Coefficients```
```                      X1      =    0.7644*F1 + 0.6448 E1
Z1

X2      =    0.7826*F1 + 0.6225 E2
Z2

Y1      =    0.8489*F2 + 0.5285 E3
Z3

Y2      =    0.8605*F2 + 0.5095 E4
Z4

```
```                         Squared Multiple Correlations
----------------------------------------------------------
Error           Total
Variable       Variance        Variance        R-squared
----------------------------------------------------------```
```             1    X1       35.921114       86.397901        0.584236
2    X2       33.423734       86.263200        0.612538
3    Y1       27.170428       97.285000        0.720713
4    Y2       25.388868       97.819200        0.740451

```
```                    Correlations among Exogenous Variables
--------------------------------
Parameter          Estimate
--------------------------------```
```                       F2    F1                1.000000

```
```
Predicted Moments of Latent Variables
```
```                                      F1                F2

F1       1.000000000       1.000000000
F2       1.000000000       1.000000000```

```                  TEST32: Vocabulary Test Data, LORD (1957)                125
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Moments between Manifest and Latent Variables
```
```                                      F1                F2

X1       7.104701757       7.104701757
X2       7.269076049       7.269076049
Y1       8.373444493       8.373444493
Y2       8.510601182       8.510601182
```
```
Latent Variable Score Regression Coefficients
```
```                                      F1                F2

X1      0.0209975428      0.0209975428
X2      0.0230885502      0.0230885502
Y1      0.0327174982      0.0327174982
Y2      0.0355868310      0.0355868310
```
```
Total Effects of Exogenous on Endogenous Variables
```
```                                      F1                F2

X1       7.104701757       0.000000000
X2       7.269076049       0.000000000
Y1       0.000000000       8.373444493
Y2       0.000000000       8.510601182
```
```
Indirect Effects of Exogenous on Endogenous Variables
```
```                                      F1                F2

X1                 0                 0
X2                 0                 0
Y1                 0                 0
Y2                 0                 0
```

```                  TEST32: Vocabulary Test Data, LORD (1957)                126
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Lagrange Multiplier and Wald Test Indices _PHI_[6:6]
Symmetric Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                          F1                     F2                     E1

F1         37.622                 37.629                 37.620
0.000   0.220          0.000  -0.110          0.000   1.563

F2         37.629                 37.636                 37.627
0.000  -0.110          0.000   0.220          0.000  -1.563

E1         37.620                 37.627                221.301  [EPS1]
0.000   1.563          0.000  -1.563

E2         37.624                 37.632                 37.602
0.000   1.600          0.000  -1.600          0.000  11.364

E3         37.626                 37.633                 12.706
0.000  -1.843          0.000   1.843          0.000  -7.289

E4         37.633                 37.639                  5.335
0.000  -1.873          0.000   1.873          0.021  -4.794

E2                     E3                     E4

F1         37.624                 37.626                 37.633
0.000   1.600          0.000  -1.843          0.000  -1.873

F2         37.632                 37.633                 37.639
0.000  -1.600          0.000   1.843          0.000   1.873

E1         37.602                 12.706                  5.335
0.000  11.364          0.000  -7.289          0.021  -4.794

E2        209.290  [EPS2]          5.335                 12.710
0.021  -4.826          0.000  -7.580

E3          5.335                146.316  [EPS3]         37.673
0.021  -4.826                                 0.000  15.681

E4         12.710                 37.673                132.173  [EPS4]
0.000  -7.580          0.000  15.681```

```                  TEST32: Vocabulary Test Data, LORD (1957)                127
Confirmatory Factor Analysis, JOERESKOG (1978, p. 452)
Hypothesis 3, JOERESKOG (1978, p. 452)
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Rank order of 10 largest Lagrange multipliers in _PHI_
```
```                 E4 : E3             E4 : F2             F2 : F2
37.6733 : 0.000     37.6386 : 0.000     37.6360 : 0.000

E3 : F2             E4 : F1             E2 : F2
37.6335 : 0.000     37.6325 : 0.000     37.6316 : 0.000

F2 : F1             E1 : F2             E3 : F1
37.6291 : 0.000     37.6267 : 0.000     37.6257 : 0.000

E2 : F1
37.6244 : 0.000

```
```            Lagrange Multiplier and Wald Test Indices _GAMMA_[4:2]
General Matrix
Univariate Tests for Constant Constraints
------------------------------------------
|  Lagrange Multiplier  or  Wald Index   |
------------------------------------------
|  Probability  | Approx Change of Value |
------------------------------------------```
```                                      F1                    F2

X1        487.532   [Z1]           SING
.      .

X2        521.653   [Z2]           SING
.      .

Y1           SING               662.106   [Z3]
.      .

Y2           SING               689.588   [Z4]
.      .
```