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Predicting Improved vs. Not Improved 1
The LOGISTIC Procedure
Data Set: WORK.ARTHRIT
Response Variable: BETTER
Response Levels: 2
Number of Observations: 84
Link Function: Logit
Response Profile
Ordered
Value BETTER Count
1 1 42
2 0 42
Deviance and Pearson Goodness-of-Fit Statistics
Pr >
Criterion DF Value Value/DF Chi-Square
Deviance 1 0.2776 0.2776 0.5983
Pearson 1 0.2637 0.2637 0.6076
Number of unique profiles: 4
Model Fitting Information and Testing Global Null Hypothesis BETA=0
Intercept
Intercept and
Criterion Only Covariates Chi-Square for Covariates
AIC 118.449 104.222 . SC 120.880 111.514 . -2 LOG L 116.449 98.222 18.227 with 2 DF (p=0.0001) Score . . 16.797 with 2 DF (p=0.0002)
Analysis of Maximum Likelihood Estimates
Parameter Standard Wald Pr > Standardized Odds
Variable DF Estimate Error Chi-Square Chi-Square Estimate Ratio
INTERCPT 1 -1.9037 0.5982 10.1286 0.0015 . . _SEX_ 1 1.4687 0.5756 6.5092 0.0107 0.372433 4.343 _TREAT_ 1 1.7817 0.5188 11.7961 0.0006 0.493956 5.940
Predicting Improved vs. Not Improved 2
The LOGISTIC Procedure
Association of Predicted Probabilities and Observed Responses
Concordant = 61.7% Somers' D = 0.480
Discordant = 13.8% Gamma = 0.635
Tied = 24.5% Tau-a = 0.243
(1764 pairs) c = 0.740
Predicting Improved vs. Not Improved 3 Testing Sex * Treatment
The LOGISTIC Procedure
Data Set: WORK.ARTHRIT
Response Variable: BETTER
Response Levels: 2
Number of Observations: 84
Link Function: Logit
Response Profile
Ordered
Value BETTER Count
1 1 42
2 0 42
Model Fitting Information and Testing Global Null Hypothesis BETA=0
Intercept
Intercept and
Criterion Only Covariates Chi-Square for Covariates
AIC 118.449 105.944 . SC 120.880 115.667 . -2 LOG L 116.449 97.944 18.505 with 3 DF (p=0.0003) Score . . 16.822 with 3 DF (p=0.0008)
Analysis of Maximum Likelihood Estimates
Parameter Standard Wald Pr > Standardized Odds
Variable DF Estimate Error Chi-Square Chi-Square Estimate Ratio
INTERCPT 1 -2.3026 1.0488 4.8200 0.0281 . . _SEX_ 1 1.9231 1.1088 3.0079 0.0829 0.487673 6.842 _TREAT_ 1 2.3026 1.1772 3.8262 0.0505 0.638372 10.000 SEXTRT 1 -0.6703 1.3151 0.2598 0.6103 -0.173637 0.512
Association of Predicted Probabilities and Observed Responses
Concordant = 61.7% Somers' D = 0.480
Discordant = 13.8% Gamma = 0.635
Tied = 24.5% Tau-a = 0.243
(1764 pairs) c = 0.740
Predicting Improved vs. Not Improved 4 Testing all interactions stepwise
The LOGISTIC Procedure
Data Set: WORK.ARTHRIT
Response Variable: BETTER
Response Levels: 2
Number of Observations: 84
Link Function: Logit
Response Profile
Ordered
Value BETTER Count
1 1 42
2 0 42
Forward Selection Procedure
Step 0. The following variables were entered:
INTERCPT _SEX_ _TREAT_ AGE
Model Fitting Information and Testing Global Null Hypothesis BETA=0
Intercept
Intercept and
Criterion Only Covariates Chi-Square for Covariates
AIC 118.449 100.063 .
SC 120.880 109.786 .
-2 LOG L 116.449 92.063 24.386 with 3 DF (p=0.0001)
Score . . 22.005 with 3 DF (p=0.0001)
Residual Chi-Square = 4.0268 with 4 DF (p=0.4024)
Step 1. Variable AGESEX entered:
Predicting Improved vs. Not Improved 5 Testing all interactions stepwise
The LOGISTIC Procedure
Model Fitting Information and Testing Global Null Hypothesis BETA=0
Intercept
Intercept and
Criterion Only Covariates Chi-Square for Covariates
AIC 118.449 98.640 .
SC 120.880 110.794 .
-2 LOG L 116.449 88.640 27.809 with 4 DF (p=0.0001)
Score . . 24.472 with 4 DF (p=0.0001)
Residual Chi-Square = 0.2903 with 3 DF (p=0.9618)
Step 2. Variable SEXTRT entered:
Model Fitting Information and Testing Global Null Hypothesis BETA=0
Intercept
Intercept and
Criterion Only Covariates Chi-Square for Covariates
AIC 118.449 100.369 .
SC 120.880 114.954 .
-2 LOG L 116.449 88.369 28.080 with 5 DF (p=0.0001)
Score . . 24.633 with 5 DF (p=0.0002)
Residual Chi-Square = 0.0305 with 2 DF (p=0.9849)
Step 3. Variable AGE2 entered:
Predicting Improved vs. Not Improved 6 Testing all interactions stepwise
The LOGISTIC Procedure
Model Fitting Information and Testing Global Null Hypothesis BETA=0
Intercept
Intercept and
Criterion Only Covariates Chi-Square for Covariates
AIC 118.449 102.350 .
SC 120.880 119.366 .
-2 LOG L 116.449 88.350 28.099 with 6 DF (p=0.0001)
Score . . 24.647 with 6 DF (p=0.0004)
Residual Chi-Square = 0.0110 with 1 DF (p=0.9166)
Step 4. Variable AGETRT entered:
Model Fitting Information and Testing Global Null Hypothesis BETA=0
Intercept
Intercept and
Criterion Only Covariates Chi-Square for Covariates
AIC 118.449 104.339 . SC 120.880 123.785 . -2 LOG L 116.449 88.339 28.110 with 7 DF (p=0.0002) Score . . 24.649 with 7 DF (p=0.0009)
NOTE: All explanatory variables have been entered into the model.
Summary of Forward Selection Procedure
Variable Number Score Pr >
Step Entered In Chi-Square Chi-Square
1 AGESEX 4 3.6874 0.0548
2 SEXTRT 5 0.2588 0.6110
3 AGE2 6 0.0194 0.8893
4 AGETRT 7 0.0110 0.9166
Predicting Improved vs. Not Improved 7 Testing all interactions stepwise
The LOGISTIC Procedure
Analysis of Maximum Likelihood Estimates
Parameter Standard Wald Pr > Standardized Odds
Variable DF Estimate Error Chi-Square Chi-Square Estimate Ratio
INTERCPT 1 -1.3492 5.4280 0.0618 0.8037 . . _SEX_ 1 -2.3273 2.9165 0.6367 0.4249 -0.590162 0.098 _TREAT_ 1 1.9655 3.0666 0.4108 0.5216 0.544916 7.138 AGE 1 -0.0329 0.1869 0.0310 0.8602 -0.231651 0.968 AGESEX 1 0.0797 0.0501 2.5241 0.1121 1.178622 1.083 AGETRT 1 0.00541 0.0517 0.0110 0.9166 0.086555 1.005 SEXTRT 1 -0.6324 1.3744 0.2117 0.6454 -0.163804 0.531 AGE2 1 0.000276 0.00177 0.0243 0.8761 0.190087 1.000
Association of Predicted Probabilities and Observed Responses
Concordant = 81.0% Somers' D = 0.629
Discordant = 18.0% Gamma = 0.636
Tied = 1.0% Tau-a = 0.318
(1764 pairs) c = 0.815
Proportional Odds Model for IMPROVE 8
The LOGISTIC Procedure
Data Set: WORK.ARTHRIT
Response Variable: IMPROVE
Response Levels: 3
Number of Observations: 84
Link Function: Logit
Response Profile
Ordered
Value IMPROVE Count
1 0 42
2 1 14
3 2 28
Score Test for the Proportional Odds Assumption
Chi-Square = 1.8833 with 2 DF (p=0.3900)
Model Fitting Information and Testing Global Null Hypothesis BETA=0
Intercept
Intercept and
Criterion Only Covariates Chi-Square for Covariates
AIC 173.916 158.029 . SC 178.778 167.753 . -2 LOG L 169.916 150.029 19.887 with 2 DF (p=0.0001) Score . . 17.868 with 2 DF (p=0.0001)
Analysis of Maximum Likelihood Estimates
Parameter Standard Wald Pr > Standardized Odds
Variable DF Estimate Error Chi-Square Chi-Square Estimate Ratio
INTERCP1 1 1.8128 0.5566 10.6072 0.0011 . . INTERCP2 1 2.6672 0.5997 19.7809 0.0001 . . _SEX_ 1 -1.3187 0.5292 6.2102 0.0127 -0.334418 0.267 _TREAT_ 1 -1.7973 0.4728 14.4493 0.0001 -0.498287 0.166
Proportional Odds Model for IMPROVE 9
The LOGISTIC Procedure
Association of Predicted Probabilities and Observed Responses
Concordant = 58.8% Somers' D = 0.438
Discordant = 15.0% Gamma = 0.593
Tied = 26.2% Tau-a = 0.271
(2156 pairs) c = 0.719