## Output from calis1a.sas

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```               Lord's data: H4- unconstrained two-factor model               1
```
```          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
```

```               Lord's data: H4- unconstrained two-factor model               2
```
```          Covariance Structure Analysis: Pattern and Initial Values

Manifest Variable Equations
Initial Estimates```
```                   X1      =     .    *F1    + 1.0000 E1
BETA1

X2      =     .    *F1    + 1.0000 E2
BETA2

Y1      =     .    *F2    + 1.0000 E3
BETA3

Y2      =     .    *F2    + 1.0000 E4
BETA4

```
```                      Variances of Exogenous Variables
-------------------------------------
Variable    Parameter      Estimate
-------------------------------------```
```                    F1                           1.000000
F2                           1.000000
E1          VE1                     .
E2          VE2                     .
E3          VE3                     .
E4          VE4                     .

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

```               Lord's data: H4- unconstrained two-factor model               3
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          1
4 Variables          Model Matrices       4
10 Informations       Parameters           9

VARIABLE              Mean           Std Dev

X1                       0       9.294821139
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942

Some initial estimates computed by instrumental variable method.

```
```                         Vector of Initial Estimates
```
```           BETA1         1    7.55181  Matrix Entry: _GAMMA_[1:1]
BETA2         2    7.65050  Matrix Entry: _GAMMA_[2:1]
BETA3         3    8.56658  Matrix Entry: _GAMMA_[3:2]
BETA4         4    8.61722  Matrix Entry: _GAMMA_[4:2]
RHO           5    0.89868  Matrix Entry: _PHI_[2:1]
VE1           6   29.36388  Matrix Entry: _PHI_[3:3]
VE2           7   27.73308  Matrix Entry: _PHI_[4:4]
VE3           8   23.89865  Matrix Entry: _PHI_[5:5]
VE4           9   23.56278  Matrix Entry: _PHI_[6:6]
```

```               Lord's data: H4- unconstrained two-factor model               4
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 9
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 0.002
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    2   0  0.001086 0.000735 0.00013       0   0.957
2    0    3   0  0.001085 1.472E-6 2.32E-6       0   0.959

Optimization Results: Iterations= 2 Function Calls= 4 Jacobian Calls= 3
Active Constraints= 0  Criterion= 0.0010849082
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```               Lord's data: H4- unconstrained two-factor model               5
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0011
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9995
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9946
Root Mean Square Residual (RMR) . . . . . . . . .     0.2720
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.1666
Chi-square = 0.7030        df = 1       Prob>chi**2 = 0.4018
Null Model Chi-square:     df = 6                  1466.5884
RMSEA Estimate  . . . . . . . . . 0.0000  90%C.I.[., 0.0974]
Probability of Close Fit  . . . . . . . . . . . .     0.6854
ECVI Estimate . . . . . . . . . . 0.0291  90%C.I.[., 0.0391]
Bentler's Comparative Fit Index . . . . . . . . .     1.0000
Normal Theory Reweighted LS Chi-square  . . . . .     0.7026
Akaike's Information Criterion. . . . . . . . . .    -1.2970
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .    -6.7724
Schwarz's Bayesian Criterion. . . . . . . . . . .    -5.7724
McDonald's (1989) Centrality. . . . . . . . . . .     1.0002
Bentler & Bonett's (1980) Non-normed Index. . . .     1.0012
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9995
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.1666
Z-Test of Wilson & Hilferty (1931). . . . . . . .     0.2363
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9971
Bollen (1988) Non-normed Index Delta2 . . . . . .     1.0002
Hoelter's (1983) Critical N . . . . . . . . . . .       3542
```

```               Lord's data: H4- unconstrained two-factor model               6
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Manifest Variable Equations```
```                  X1      =     7.5007*F1    +  1.0000 E1
Std Err       0.3234 BETA1
t Value      23.1948

X2      =     7.7027*F1    +  1.0000 E2
Std Err       0.3206 BETA2
t Value      24.0237

Y1      =     8.5095*F2    +  1.0000 E3
Std Err       0.3269 BETA3
t Value      26.0273

Y2      =     8.6751*F2    +  1.0000 E4
Std Err       0.3256 BETA4
t Value      26.6431

```
```                      Variances of Exogenous Variables
---------------------------------------------------------------------
Standard
Variable    Parameter      Estimate          Error          t Value
---------------------------------------------------------------------```
```    F1                           1.000000               0           0.000
F2                           1.000000               0           0.000
E1          VE1             30.133758        2.470144          12.199
E2          VE2             26.932169        2.430580          11.081
E3          VE3             24.874037        2.359840          10.541
E4          VE4             22.562562        2.350252           9.600

```
```                    Covariances among Exogenous Variables
-----------------------------------------------------------------
Standard
Parameter          Estimate          Error          t Value
-----------------------------------------------------------------```
```      F2    F1    RHO          0.898551        0.018649          48.181
```

```               Lord's data: H4- unconstrained two-factor model               7
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Equations with Standardized Coefficients```
```                   X1      =    0.8070*F1    + 0.5906 E1
BETA1

X2      =    0.8293*F1    + 0.5588 E2
BETA2

Y1      =    0.8627*F2    + 0.5057 E3
BETA3

Y2      =    0.8771*F2    + 0.4803 E4
BETA4

```
```                         Squared Multiple Correlations
----------------------------------------------------------
Error           Total
Variable       Variance        Variance        R-squared
----------------------------------------------------------```
```             1    X1       30.133758       86.393709        0.651204
2    X2       26.932169       86.263207        0.687791
3    Y1       24.874037       97.285006        0.744318
4    Y2       22.562562       97.819204        0.769344

```
```                    Correlations among Exogenous Variables
---------------------------------
Parameter          Estimate
---------------------------------```
```                      F2    F1    RHO          0.898551
```

```               Lord's data: H4- unconstrained two-factor model               8
```
```          Covariance Structure Analysis: Pattern and Initial Values

RAM Model Statement
-------------------------------
Matrix         Rows & Cols          Matrix Type```
``` TERM   1-----------------------------------------------------------
1    _IDE_          4       6    IDENTITY
2    _A_            6       6    UPPER          IMINUSINV
3    _P_            6       6    SYMMETRIC
```

```               Lord's data: H4- unconstrained two-factor model               9
```
```          Covariance Structure Analysis: Pattern and Initial Values

RAM Pattern and Values
------------------------------------------------------
Term &
Matrix     Row & Column    Parameter      Estimate
------------------------------------------------------```
```             1      2       1       5    BETA1                   .
X1      F1
1      2       2       5    BETA2                   .
X2      F1
1      2       3       6    BETA3                   .
Y1      F2
1      2       4       6    BETA4                   .
Y2      F2

1      3       1       1    VE1                     .
E1      E1
1      3       2       2    VE2                     .
E2      E2
1      3       3       3    VE3                     .
E3      E3
1      3       4       4    VE4                     .
E4      E4
1      3       5       5        .            1.000000
D1      D1
1      3       6       5    RHO                     .
D2      D1
1      3       6       6        .            1.000000
D2      D2

```

```               Lord's data: H4- unconstrained two-factor model              10
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                   649 Observations       Model Terms          1
4 Variables          Model Matrices       3
10 Informations       Parameters           9

VARIABLE              Mean           Std Dev

X1                       0       9.294821139
X2                       0       9.287798447
Y1                       0       9.863315872
Y2                       0       9.890358942

Some initial estimates computed by instrumental variable method.

```
```                         Vector of Initial Estimates
```
```             BETA1         1    7.55181  Matrix Entry: _A_[1:5]
BETA2         2    7.65050  Matrix Entry: _A_[2:5]
BETA3         3    8.56658  Matrix Entry: _A_[3:6]
BETA4         4    8.61722  Matrix Entry: _A_[4:6]
VE1           5   29.36388  Matrix Entry: _P_[1:1]
VE2           6   27.73308  Matrix Entry: _P_[2:2]
VE3           7   23.89865  Matrix Entry: _P_[3:3]
VE4           8   23.56278  Matrix Entry: _P_[4:4]
RHO           9    0.89868  Matrix Entry: _P_[6:5]
```

```               Lord's data: H4- unconstrained two-factor model              11
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```                       Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Number of Parameter Estimates 9
Number of Functions (Observations) 10

Optimization Start: Active Constraints= 0  Criterion= 0.002
```
`        Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho`
```           1    0    2   0  0.001086 0.000735 0.00013       0   0.957
2    0    3   0  0.001085 1.472E-6 2.32E-6       0   0.959

Optimization Results: Iterations= 2 Function Calls= 4 Jacobian Calls= 3
Active Constraints= 0  Criterion= 0.0010849082
```
`NOTE:  ABSGCONV convergence criterion satisfied.`

```               Lord's data: H4- unconstrained two-factor model              12
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation
```
```         Fit criterion . . . . . . . . . . . . . . . . . .     0.0011
Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9995
GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9946
Root Mean Square Residual (RMR) . . . . . . . . .     0.2720
Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.1666
Chi-square = 0.7030        df = 1       Prob>chi**2 = 0.4018
Null Model Chi-square:     df = 6                  1466.5884
RMSEA Estimate  . . . . . . . . . 0.0000  90%C.I.[., 0.0974]
Probability of Close Fit  . . . . . . . . . . . .     0.6854
ECVI Estimate . . . . . . . . . . 0.0291  90%C.I.[., 0.0391]
Bentler's Comparative Fit Index . . . . . . . . .     1.0000
Normal Theory Reweighted LS Chi-square  . . . . .     0.7026
Akaike's Information Criterion. . . . . . . . . .    -1.2970
Bozdogan's (1987) CAIC. . . . . . . . . . . . . .    -6.7724
Schwarz's Bayesian Criterion. . . . . . . . . . .    -5.7724
McDonald's (1989) Centrality. . . . . . . . . . .     1.0002
Bentler & Bonett's (1980) Non-normed Index. . . .     1.0012
Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9995
James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.1666
Z-Test of Wilson & Hilferty (1931). . . . . . . .     0.2363
Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9971
Bollen (1988) Non-normed Index Delta2 . . . . . .     1.0002
Hoelter's (1983) Critical N . . . . . . . . . . .       3542
```

```               Lord's data: H4- unconstrained two-factor model              13
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

RAM Pattern and Values
------------------------------------------------------------------------
Term &                                         Standard
Matrix Row & Column Parameter    Estimate        Error        t Value
------------------------------------------------------------------------```
```    1    2     1     5  BETA1          7.500663      0.323377        23.195
X1    F1
1    2     2     5  BETA2          7.702664      0.320628        24.024
X2    F1
1    2     3     6  BETA3          8.509464      0.326943        26.027
Y1    F2
1    2     4     6  BETA4          8.675059      0.325603        26.643
Y2    F2

1    3     1     1  VE1           30.133758      2.470144        12.199
E1    E1
1    3     2     2  VE2           26.932169      2.430580        11.081
E2    E2
1    3     3     3  VE3           24.874037      2.359840        10.541
E3    E3
1    3     4     4  VE4           22.562562      2.350252         9.600
E4    E4
1    3     5     5      .          1.000000             0         0.000
D1    D1
1    3     6     5  RHO            0.898551      0.018649        48.181
D2    D1
1    3     6     6      .          1.000000             0         0.000
D2    D2

```
```                          Standardized Coefficients
-----------------------------------------
Row & Column    Parameter      Estimate
-----------------------------------------```
```                     1       5    BETA1            0.806972
X1      F1
2       5    BETA2            0.829332
X2      F1
3       6    BETA3            0.862739
Y1      F2
4       6    BETA4            0.877123
Y2      F2
```

```               Lord's data: H4- unconstrained two-factor model              14
```
```         Covariance Structure Analysis: Maximum Likelihood Estimation

Squared Multiple Correlations
----------------------------------------------------------
Error           Total
Variable       Variance        Variance        R-squared
----------------------------------------------------------```
```             1    E1       30.133758       86.393709        0.651204
2    E2       26.932169       86.263207        0.687791
3    E3       24.874037       97.285006        0.744318
4    E4       22.562562       97.819204        0.769344

```
```                    Correlations among Exogenous Variables
-------------------------------------------------
Row & Column        Parameter          Estimate
-------------------------------------------------```
```                 6       5    D2    D1    RHO          0.898551
```