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='Fail' 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 Gone 1 0.3878 0.1716 5.1059 0.0238
Intercept Pass 1 1.4123 0.1477 91.4183 <.0001
missused Gone 1 0.7209 0.2641 7.4506 0.0063
missused Pass 1 -0.6461 0.2573 6.3054 0.0120

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
missused Gone 2.056 1.225 3.451
missused Pass 0.524 0.317 0.868

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_Gone Intercept: outcome=Gone 0.388
2 Intercept_Pass Intercept: outcome=Pass 1.412
3 missused_Gone Any of hsgpa hscalc precalc missing: outcome=Gone 0.721
4 missused_Pass Any of hsgpa hscalc precalc missing: outcome=Pass -0.646
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='Fail' 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 Gone 1 0.3878 0.1716 5.1059 0.0238
Intercept Pass 1 1.4123 0.1477 91.4183 <.0001
missused Gone 1 0.7209 0.2641 7.4506 0.0063
missused Pass 1 -0.6461 0.2573 6.3054 0.0120

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
missused Gone 2.056 1.225 3.451
missused Pass 0.524 0.317 0.868

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='Fail' 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 Gone 1 2.4602 3.2708 0.5658 0.4519
Intercept Pass 1 -12.0793 2.9528 16.7346 <.0001
hsgpa Gone 1 0.0410 0.0451 0.8274 0.3630
hsgpa Pass 1 0.1385 0.0403 11.8272 0.0006
hscalc Gone 1 -0.0343 0.0183 3.5037 0.0612
hscalc Pass 1 0.0430 0.0169 6.4593 0.0110
precalc Gone 1 -0.1307 0.1220 1.1469 0.2842
precalc Pass 1 0.2372 0.1068 4.9332 0.0263
mtongue Gone 1 -2.8199 0.7647 13.5988 0.0002
mtongue Pass 1 -1.9585 0.7551 6.7265 0.0095

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsgpa Gone 1.042 0.954 1.138
hsgpa Pass 1.149 1.061 1.243
hscalc Gone 0.966 0.932 1.002
hscalc Pass 1.044 1.010 1.079
precalc Gone 0.877 0.691 1.115
precalc Pass 1.268 1.028 1.563
mtongue Gone 0.060 0.013 0.267
mtongue Pass 0.141 0.032 0.620

Prediction of Performance in First-year Calculus

Replicate hsgpa hscalc precalc mtongue 0.05/8 = .00625

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.REPLIC
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='Fail' 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 Gone 1 -0.5251 2.6848 0.0383 0.8449
Intercept Pass 1 -12.8640 2.5076 26.3167 <.0001
hsgpa Gone 1 0.0411 0.0389 1.1120 0.2916
hsgpa Pass 1 0.1391 0.0364 14.6003 0.0001
hscalc Gone 1 -0.0291 0.0172 2.8782 0.0898
hscalc Pass 1 0.0317 0.0167 3.6065 0.0576
precalc Gone 1 -0.0547 0.1130 0.2347 0.6281
precalc Pass 1 0.2068 0.1005 4.2305 0.0397
mtongue Gone 1 0.000703 0.3959 0.0000 0.9986
mtongue Pass 1 -0.2323 0.3582 0.4207 0.5166

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsgpa Gone 1.042 0.965 1.125
hsgpa Pass 1.149 1.070 1.234
hscalc Gone 0.971 0.939 1.005
hscalc Pass 1.032 0.999 1.067
precalc Gone 0.947 0.759 1.181
precalc Pass 1.230 1.010 1.498
mtongue Gone 1.001 0.461 2.174
mtongue Pass 0.793 0.393 1.600