Results: multilogit.sas

Prediction of Performance in First-year Calculus: Exploratory Sample

Outcome by passed just to check

The FREQ Procedure

The Freq Procedure

Table outcome * passed

Cross-Tabular Freq Table

Frequency
Table of outcome by passed
outcome passed(Passed the course)
No Yes Total
Fail
90
0
90
Gone
184
0
184
Pass
0
305
305
Total
274
305
579

Prediction of Performance in First-year Calculus: Exploratory Sample

Missused by Outcome with proc freq

The FREQ Procedure

The Freq Procedure

Table missused * outcome

Cross-Tabular Freq Table

Frequency
Row Pct
Table of missused by outcome
missused(Any of hsgpa hscalc precalc missing) outcome
Fail Gone Pass Total
No
57
15.20
84
22.40
234
62.40
375
 
Yes
33
16.18
100
49.02
71
34.80
204
 
Total
90
184
305
579

Statistics for Table of missused by outcome

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 2 48.6430 <.0001
Likelihood Ratio Chi-Square 2 48.4279 <.0001
Mantel-Haenszel Chi-Square 1 19.7821 <.0001
Phi Coefficient   0.2898  
Contingency Coefficient   0.2784  
Cramer's V   0.2898  

Sample Size = 579

Prediction of Performance in First-year Calculus: Exploratory Sample

Misssused by Outcome with proc logistic

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.MATHEX
Response Variable outcome
Number of Response Levels 3
Model generalized logit
Optimization Technique Newton-Raphson

Observations Summary

Number of Observations Read 579
Number of Observations Used 579

Response Profile

Response Profile
Ordered
Value		 outcome Total
Frequency
1 Fail 90
2 Gone 184
3 Pass 305

Logits modeled use outcome='Pass' as the reference category.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 1151.936 1107.508
SC 1160.659 1124.953
-2 Log L 1147.936 1099.508

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 48.4279 2 <.0001
Score 48.6430 2 <.0001
Wald 46.4209 2 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
missused 2 46.4209 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept Fail 1 -1.4123 0.1477 91.4183 <.0001
Intercept Gone 1 -1.0245 0.1272 64.8777 <.0001
missused Fail 1 0.6461 0.2573 6.3054 0.0120
missused Gone 1 1.3670 0.2007 46.4119 <.0001

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
missused Fail 1.908 1.152 3.159
missused Gone 3.924 2.648 5.814

Wald Test for Contrasts

Contrast Test Results
Contrast DF Wald
Chi-Square		 Pr > ChiSq
Hsgpa, hscalc or precalc missing 2 46.4209 <.0001

Prediction of Performance in First-year Calculus: Exploratory Sample

Misssused by Outcome with proc logistic

The Print Procedure

Data Set WORK.DATA2

Obs _NAME_ _LABEL_ outcome
1 Intercept_Fail Intercept: outcome=Fail -1.412
2 Intercept_Gone Intercept: outcome=Gone -1.025
3 missused_Fail Any of hsgpa hscalc precalc missing: outcome=Fail 0.646
4 missused_Gone Any of hsgpa hscalc precalc missing: outcome=Gone 1.367
5 _LNLIKE_ Model Log Likelihood -549.754

Prediction of Performance in First-year Calculus: Exploratory Sample

Contrast versus test

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.MATHEX
Response Variable outcome
Number of Response Levels 3
Model generalized logit
Optimization Technique Newton-Raphson

Observations Summary

Number of Observations Read 579
Number of Observations Used 579

Response Profile

Response Profile
Ordered
Value		 outcome Total
Frequency
1 Fail 90
2 Gone 184
3 Pass 305

Logits modeled use outcome='Pass' as the reference category.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 1151.936 1107.508
SC 1160.659 1124.953
-2 Log L 1147.936 1099.508

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 48.4279 2 <.0001
Score 48.6430 2 <.0001
Wald 46.4209 2 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
missused 2 46.4209 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept Fail 1 -1.4123 0.1477 91.4183 <.0001
Intercept Gone 1 -1.0245 0.1272 64.8777 <.0001
missused Fail 1 0.6461 0.2573 6.3054 0.0120
missused Gone 1 1.3670 0.2007 46.4119 <.0001

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
missused Fail 1.908 1.152 3.159
missused Gone 3.924 2.648 5.814

Wald Test for Contrasts

Contrast Test Results
Contrast DF Wald
Chi-Square		 Pr > ChiSq
Missused method 1 2 46.4209 <.0001

Test Statement Results

Linear Hypotheses Testing Results
Label Wald
Chi-Square		 DF Pr > ChiSq
MissusedMethod2 46.4209 2 <.0001

Prediction of Performance in First-year Calculus: Exploratory Sample

Estimate Probabilities using output from proc logistic

The IML Procedure

Fail_Gone_Pass

  Fail Gone Pass
Not missing: 0.151996 0.2240018 0.6240023

Fail_Gone_Pass

  Fail Gone Pass
Yes Missing: 0.1617602 0.4902007 0.3480391

Prediction of Performance in First-year Calculus: Exploratory Sample

Missused by outcome again for comparison

The FREQ Procedure

The Freq Procedure

Table missused * outcome

Cross-Tabular Freq Table

Frequency
Row Pct
Table of missused by outcome
missused(Any of hsgpa hscalc precalc missing) outcome
Fail Gone Pass Total
No
57
15.20
84
22.40
234
62.40
375
 
Yes
33
16.18
100
49.02
71
34.80
204
 
Total
90
184
305
579

Prediction of Performance in First-year Calculus: Exploratory Sample

hsgpa hscalc precalc mtongue

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.MATHEX
Response Variable outcome
Number of Response Levels 3
Model generalized logit
Optimization Technique Newton-Raphson

Observations Summary

Number of Observations Read 579
Number of Observations Used 370

Response Profile

Response Profile
Ordered
Value		 outcome Total
Frequency
1 Fail 57
2 Gone 81
3 Pass 232

Logits modeled use outcome='Pass' as the reference category.

Note:209 observations were deleted due to missing values for the response or explanatory variables.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 679.897 542.957
SC 687.724 582.092
-2 Log L 675.897 522.957

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 152.9401 8 <.0001
Score 128.0475 8 <.0001
Wald 92.2926 8 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
hsgpa 2 14.4271 0.0007
hscalc 2 25.0219 <.0001
precalc 2 14.1642 0.0008
mtongue 2 15.9958 0.0003

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept Fail 1 12.0793 2.9528 16.7346 <.0001
Intercept Gone 1 14.5396 2.7212 28.5479 <.0001
hsgpa Fail 1 -0.1385 0.0403 11.8272 0.0006
hsgpa Gone 1 -0.0975 0.0370 6.9315 0.0085
hscalc Fail 1 -0.0430 0.0169 6.4593 0.0110
hscalc Gone 1 -0.0772 0.0156 24.4284 <.0001
precalc Fail 1 -0.2372 0.1068 4.9332 0.0263
precalc Gone 1 -0.3679 0.1025 12.8876 0.0003
mtongue Fail 1 1.9585 0.7551 6.7265 0.0095
mtongue Gone 1 -0.8614 0.3523 5.9779 0.0145

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsgpa Fail 0.871 0.805 0.942
hsgpa Gone 0.907 0.844 0.975
hscalc Fail 0.958 0.927 0.990
hscalc Gone 0.926 0.898 0.954
precalc Fail 0.789 0.640 0.972
precalc Gone 0.692 0.566 0.846
mtongue Fail 7.088 1.614 31.140
mtongue Gone 0.423 0.212 0.843

Prediction of Performance in First-year Calculus: Exploratory Sample

Different coefficients for Gone and Fail?

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.MATHEX
Response Variable outcome
Number of Response Levels 3
Model generalized logit
Optimization Technique Newton-Raphson

Observations Summary

Number of Observations Read 579
Number of Observations Used 370

Response Profile

Response Profile
Ordered
Value		 outcome Total
Frequency
1 Fail 57
2 Gone 81
3 Pass 232

Logits modeled use outcome='Pass' as the reference category.

Note:209 observations were deleted due to missing values for the response or explanatory variables.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 679.897 542.957
SC 687.724 582.092
-2 Log L 675.897 522.957

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 152.9401 8 <.0001
Score 128.0475 8 <.0001
Wald 92.2926 8 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
hsgpa 2 14.4271 0.0007
hscalc 2 25.0219 <.0001
precalc 2 14.1642 0.0008
mtongue 2 15.9958 0.0003

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept Fail 1 12.0793 2.9528 16.7346 <.0001
Intercept Gone 1 14.5396 2.7212 28.5479 <.0001
hsgpa Fail 1 -0.1385 0.0403 11.8272 0.0006
hsgpa Gone 1 -0.0975 0.0370 6.9315 0.0085
hscalc Fail 1 -0.0430 0.0169 6.4593 0.0110
hscalc Gone 1 -0.0772 0.0156 24.4284 <.0001
precalc Fail 1 -0.2372 0.1068 4.9332 0.0263
precalc Gone 1 -0.3679 0.1025 12.8876 0.0003
mtongue Fail 1 1.9585 0.7551 6.7265 0.0095
mtongue Gone 1 -0.8614 0.3523 5.9779 0.0145

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsgpa Fail 0.871 0.805 0.942
hsgpa Gone 0.907 0.844 0.975
hscalc Fail 0.958 0.927 0.990
hscalc Gone 0.926 0.898 0.954
precalc Fail 0.789 0.640 0.972
precalc Gone 0.692 0.566 0.846
mtongue Fail 7.088 1.614 31.140
mtongue Gone 0.423 0.212 0.843

Test Statement Results

Linear Hypotheses Testing Results
Label Wald
Chi-Square		 DF Pr > ChiSq
DiffOverall 17.0587 4 0.0019
Diff_hsgpa 0.8274 1 0.3630
Diff_hscalc 3.5037 1 0.0612
Diff_precalc 1.1469 1 0.2842
Diff_mtongue 13.5988 1 0.0002

Prediction of Performance in First-year Calculus: Replication Sample

Replicate hsgpa hscalc precalc calc mtongue 0.05/8 = .00625

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.MATHREP
Response Variable outcome
Number of Response Levels 3
Model generalized logit
Optimization Technique Newton-Raphson

Observations Summary

Number of Observations Read 579
Number of Observations Used 385

Response Profile

Response Profile
Ordered
Value		 outcome Total
Frequency
1 Fail 65
2 Gone 95
3 Pass 225

Logits modeled use outcome='Pass' as the reference category.

Note:194 observations were deleted due to missing values for the response or explanatory variables.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 742.845 653.733
SC 750.752 693.266
-2 Log L 738.845 633.733

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 105.1118 8 <.0001
Score 91.8145 8 <.0001
Wald 74.7659 8 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
hsgpa 2 17.6578 0.0001
hscalc 2 16.7229 0.0002
precalc 2 9.6883 0.0079
mtongue 2 0.6988 0.7051

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept Fail 1 12.8640 2.5076 26.3167 <.0001
Intercept Gone 1 12.3389 2.2830 29.2093 <.0001
hsgpa Fail 1 -0.1391 0.0364 14.6003 0.0001
hsgpa Gone 1 -0.0980 0.0324 9.1308 0.0025
hscalc Fail 1 -0.0317 0.0167 3.6065 0.0576
hscalc Gone 1 -0.0609 0.0149 16.6687 <.0001
precalc Fail 1 -0.2068 0.1005 4.2305 0.0397
precalc Gone 1 -0.2615 0.0914 8.1764 0.0042
mtongue Fail 1 0.2323 0.3582 0.4207 0.5166
mtongue Gone 1 0.2330 0.3265 0.5095 0.4753

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsgpa Fail 0.870 0.810 0.935
hsgpa Gone 0.907 0.851 0.966
hscalc Fail 0.969 0.938 1.001
hscalc Gone 0.941 0.914 0.969
precalc Fail 0.813 0.668 0.990
precalc Gone 0.770 0.644 0.921
mtongue Fail 1.262 0.625 2.546
mtongue Gone 1.262 0.666 2.394

Test Statement Results

Linear Hypotheses Testing Results
Label Wald
Chi-Square		 DF Pr > ChiSq
Diff_mtongue 0.0000 1 0.9986