Results: MathLogReg4.sas

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

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

Logistic regression with more than 2 resp. categories

One at a time cat IVs with proc freq

The FREQ Procedure

The FREQ Procedure

Table course2 * outcome

Cross-Tabular Freq Table

Frequency
Row Pct
Table of course2 by outcome
course2 outcome
Fail Gone Pass Total
Catch-up
9
15.25
35
59.32
15
25.42
59
 
Mainstrm
61
16.35
88
23.59
224
60.05
373
 
Elite
6
15.38
2
5.13
31
79.49
39
 
Total
76
125
270
471
Frequency Missing = 108

Statistics for Table of course2 by outcome

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 4 46.2026 <.0001
Likelihood Ratio Chi-Square 4 45.7760 <.0001
Mantel-Haenszel Chi-Square 1 13.4884 0.0002
Phi Coefficient   0.3132  
Contingency Coefficient   0.2989  
Cramer's V   0.2215  

Effective Sample Size = 471
Frequency Missing = 108

WARNING: 19% of the data are missing.

Table sex * outcome

Cross-Tabular Freq Table

Frequency
Row Pct
Table of sex by outcome
sex outcome
Fail Gone Pass Total
Female
45
16.92
73
27.44
148
55.64
266
 
Male
43
15.09
95
33.33
147
51.58
285
 
Total
88
168
295
551
Frequency Missing = 28

Statistics for Table of sex by outcome

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 2 2.2773 0.3202
Likelihood Ratio Chi-Square 2 2.2828 0.3194
Mantel-Haenszel Chi-Square 1 0.1233 0.7254
Phi Coefficient   0.0643  
Contingency Coefficient   0.0642  
Cramer's V   0.0643  

Effective Sample Size = 551
Frequency Missing = 28

Table ethnic * outcome

Cross-Tabular Freq Table

Frequency
Row Pct
Table of ethnic by outcome
ethnic(Judged Nationality of name) outcome
Fail Gone Pass Total
Asian
21
16.03
44
33.59
66
50.38
131
 
Eastern European
13
20.63
17
26.98
33
52.38
63
 
European not Eastern
35
17.95
53
27.18
107
54.87
195
 
Middle-Eastern and Pakistani
11
15.28
22
30.56
39
54.17
72
 
East Indian
6
7.69
25
32.05
47
60.26
78
 
Other and DK
4
10.00
23
57.50
13
32.50
40
 
Total
90
184
305
579

Statistics for Table of ethnic by outcome

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 10 20.2180 0.0273
Likelihood Ratio Chi-Square 10 19.8317 0.0309
Mantel-Haenszel Chi-Square 1 0.4698 0.4931
Phi Coefficient   0.1869  
Contingency Coefficient   0.1837  
Cramer's V   0.1321  

Sample Size = 579

Table tongue * outcome

Cross-Tabular Freq Table

Frequency
Row Pct
Table of tongue by outcome
tongue(Mother Tongue (Eng or Other)) outcome
Fail Gone Pass Total
English
74
18.41
113
28.11
215
53.48
402
 
Other
14
9.40
55
36.91
80
53.69
149
 
Total
88
168
295
551
Frequency Missing = 28

Statistics for Table of tongue by outcome

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 2 8.2920 0.0158
Likelihood Ratio Chi-Square 2 8.8198 0.0122
Mantel-Haenszel Chi-Square 1 1.6654 0.1969
Phi Coefficient   0.1227  
Contingency Coefficient   0.1218  
Cramer's V   0.1227  

Effective Sample Size = 551
Frequency Missing = 28

Table hsmiss * outcome

Cross-Tabular Freq Table

Frequency
Row Pct
Table of hsmiss by outcome
hsmiss(Missing Any High School Data) outcome
Fail Gone Pass Total
No
66
15.17
112
25.75
257
59.08
435
 
Yes
24
16.67
72
50.00
48
33.33
144
 
Total
90
184
305
579

Statistics for Table of hsmiss by outcome

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 2 33.7946 <.0001
Likelihood Ratio Chi-Square 2 33.3038 <.0001
Mantel-Haenszel Chi-Square 1 14.7239 0.0001
Phi Coefficient   0.2416  
Contingency Coefficient   0.2348  
Cramer's V   0.2416  

Sample Size = 579

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

Multinomial logit model 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 1122.632
SC 1160.659 1140.077
-2 Log L 1147.936 1114.632

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 33.3038 2 <.0001
Score 33.7946 2 <.0001
Wald 32.1439 2 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
hsmiss 2 32.1439 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept Fail 1 -1.3594 0.1380 97.0471 <.0001
Intercept Gone 1 -0.8306 0.1132 53.8127 <.0001
hsmiss Fail 1 0.6663 0.2856 5.4441 0.0196
hsmiss Gone 1 1.2360 0.2180 32.1359 <.0001

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsmiss Fail 1.947 1.112 3.407
hsmiss Gone 3.442 2.245 5.277

Wald Test for Contrasts

Contrast Test Results
Contrast DF Wald
Chi-Square		 Pr > ChiSq
HS Missing method 1 2 32.1439 <.0001

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

Multinomial logit model with proc logistic

The PRINT Procedure

Data Set WORK.DATA6

_NAME_ _LABEL_ outcome
Intercept_Fail Intercept: outcome=Fail -1.359
Intercept_Gone Intercept: outcome=Gone -0.831
hsmiss_Fail Missing Any High School Data: outcome=Fail 0.666
hsmiss_Gone Missing Any High School Data: outcome=Gone 1.236
_LNLIKE_ Model Log Likelihood -557.316

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

Multinomial logit model 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 1122.632
SC 1160.659 1140.077
-2 Log L 1147.936 1114.632

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 33.3038 2 <.0001
Score 33.7946 2 <.0001
Wald 32.1439 2 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
hsmiss 2 32.1439 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept Fail 1 -1.3594 0.1380 97.0471 <.0001
Intercept Gone 1 -0.8306 0.1132 53.8127 <.0001
hsmiss Fail 1 0.6663 0.2856 5.4441 0.0196
hsmiss Gone 1 1.2360 0.2180 32.1359 <.0001

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsmiss Fail 1.947 1.112 3.407
hsmiss Gone 3.442 2.245 5.277

Wald Test for Contrasts

Contrast Test Results
Contrast DF Wald
Chi-Square		 Pr > ChiSq
HS Missing method 1 2 32.1439 <.0001

Test Statement Results

Linear Hypotheses Testing Results
Label Wald
Chi-Square		 DF Pr > ChiSq
HS_MissingMethod2 32.1439 2 <.0001

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

Estimate Probabilities using output from proc catmod

The IML Procedure

Fail_Gone_Pass

  Fail Gone Pass
No Missing HS Data: 0.1517278 0.2574661 0.5908062

Fail_Gone_Pass

  Fail Gone Pass
Yes Missing HS Data: 0.1666786 0.4999798 0.3333416

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

Hsmiss by outcome again for comparison

The FREQ Procedure

The FREQ Procedure

Table hsmiss * outcome

Cross-Tabular Freq Table

Frequency
Row Pct
Table of hsmiss by outcome
hsmiss(Missing Any High School Data) outcome
Fail Gone Pass Total
No
66
15.17
112
25.75
257
59.08
435
 
Yes
24
16.67
72
50.00
48
33.33
144
 
Total
90
184
305
579

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

HS variables

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 435

Response Profile

Response Profile
Ordered
Value		 outcome Total
Frequency
1 Fail 66
2 Gone 112
3 Pass 257

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

Note:144 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 827.348 706.181
SC 835.498 738.784
-2 Log L 823.348 690.181

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 133.1668 6 <.0001
Score 112.0573 6 <.0001
Wald 84.2616 6 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
hsgpa 2 20.4749 <.0001
hscalc 2 22.2033 <.0001
hsengl 2 0.8757 0.6454

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept Fail 1 13.3871 2.5867 26.7839 <.0001
Intercept Gone 1 16.5896 2.3505 49.8149 <.0001
hsgpa Fail 1 -0.1487 0.0425 12.2317 0.0005
hsgpa Gone 1 -0.1502 0.0375 16.0254 <.0001
hscalc Fail 1 -0.0485 0.0161 9.0375 0.0026
hscalc Gone 1 -0.0643 0.0141 20.7653 <.0001
hsengl Fail 1 0.00782 0.0214 0.1331 0.7152
hsengl Gone 1 -0.0119 0.0184 0.4196 0.5171

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsgpa Fail 0.862 0.793 0.937
hsgpa Gone 0.860 0.799 0.926
hscalc Fail 0.953 0.923 0.983
hscalc Gone 0.938 0.912 0.964
hsengl Fail 1.008 0.966 1.051
hsengl Gone 0.988 0.953 1.024

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

HS gpa and calc + course2

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 375

Response Profile

Response Profile
Ordered
Value		 outcome Total
Frequency
1 Fail 57
2 Gone 84
3 Pass 234

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

Note:204 observations were deleted due to missing values for the response or explanatory variables.

Class Level Information

Class Level Information
Class Value Design Variables
course2 Catch-up 1 0
  Elite 0 1
  Mainstrm 0 0

Convergence Status

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

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 690.819 585.522
SC 698.673 624.791
-2 Log L 686.819 565.522

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 121.2971 8 <.0001
Score 104.0573 8 <.0001
Wald 77.3057 8 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
hsgpa 2 17.6424 0.0001
hscalc 2 28.4400 <.0001
course2 4 2.4278 0.6576

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter   outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept   Fail 1 13.5345 2.8068 23.2528 <.0001
Intercept   Gone 1 14.6775 2.6323 31.0901 <.0001
hsgpa   Fail 1 -0.1331 0.0388 11.7609 0.0006
hsgpa   Gone 1 -0.1247 0.0358 12.0917 0.0005
hscalc   Fail 1 -0.0588 0.0169 12.0445 0.0005
hscalc   Gone 1 -0.0789 0.0155 26.0341 <.0001
course2 Catch-up Fail 1 -0.3161 0.7021 0.2027 0.6525
course2 Catch-up Gone 1 0.0165 0.5820 0.0008 0.9774
course2 Elite Fail 1 0.0862 0.5647 0.0233 0.8786
course2 Elite Gone 1 -1.0842 0.7858 1.9036 0.1677

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsgpa Fail 0.875 0.811 0.945
hsgpa Gone 0.883 0.823 0.947
hscalc Fail 0.943 0.912 0.975
hscalc Gone 0.924 0.897 0.953
course2 Catch-up vs Mainstrm Fail 0.729 0.184 2.886
course2 Catch-up vs Mainstrm Gone 1.017 0.325 3.181
course2 Elite vs Mainstrm Fail 1.090 0.360 3.297
course2 Elite vs Mainstrm Gone 0.338 0.072 1.578

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

HS gpa and calc + diagnostic 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 375

Response Profile

Response Profile
Ordered
Value		 outcome Total
Frequency
1 Fail 57
2 Gone 84
3 Pass 234

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

Note:204 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 690.819 570.945
SC 698.673 610.215
-2 Log L 686.819 550.945

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 135.8738 8 <.0001
Score 112.6955 8 <.0001
Wald 83.0981 8 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
hsgpa 2 14.5724 0.0007
hscalc 2 19.6498 <.0001
precalc 2 8.7550 0.0126
calc 2 3.5698 0.1678

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept Fail 1 13.2646 2.7880 22.6358 <.0001
Intercept Gone 1 14.4527 2.6767 29.1539 <.0001
hsgpa Fail 1 -0.1247 0.0388 10.3285 0.0013
hsgpa Gone 1 -0.1133 0.0365 9.6348 0.0019
hscalc Fail 1 -0.0492 0.0170 8.3304 0.0039
hscalc Gone 1 -0.0664 0.0156 18.0393 <.0001
precalc Fail 1 -0.2425 0.1118 4.7033 0.0301
precalc Gone 1 -0.2782 0.1049 7.0300 0.0080
calc Fail 1 -0.0113 0.0804 0.0196 0.8887
calc Gone 1 -0.1469 0.0802 3.3545 0.0670

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsgpa Fail 0.883 0.818 0.953
hsgpa Gone 0.893 0.831 0.959
hscalc Fail 0.952 0.921 0.984
hscalc Gone 0.936 0.908 0.965
precalc Fail 0.785 0.630 0.977
precalc Gone 0.757 0.616 0.930
calc Fail 0.989 0.845 1.158
calc Gone 0.863 0.738 1.010

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

Try gender, ethnic and mother tongue controlling for good stuff

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.

Class Level Information

Class Level Information
Class Value Design Variables
ethnic Asian 1 0 0 0 0
  East Indian 0 0 0 0 0
  Eastern European 0 1 0 0 0
  European not Eastern 0 0 1 0 0
  Middle-Eastern and Pakistani 0 0 0 1 0
  Other and DK 0 0 0 0 1

Convergence Status

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

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 679.897 556.063
SC 687.724 642.160
-2 Log L 675.897 512.063

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 163.8346 20 <.0001
Score 138.3813 20 <.0001
Wald 98.7535 20 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
hsgpa 2 10.4338 0.0054
hscalc 2 25.9938 <.0001
precalc 2 15.3070 0.0005
ethnic 10 8.7146 0.5594
gender 2 0.7564 0.6851
mtongue 2 13.4091 0.0012

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter   outcome DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept   Fail 1 10.1216 3.1497 10.3263 0.0013
Intercept   Gone 1 14.8993 2.9069 26.2700 <.0001
hsgpa   Fail 1 -0.1176 0.0416 7.9740 0.0047
hsgpa   Gone 1 -0.0924 0.0387 5.6941 0.0170
hscalc   Fail 1 -0.0500 0.0177 7.9751 0.0047
hscalc   Gone 1 -0.0816 0.0163 24.9061 <.0001
precalc   Fail 1 -0.2555 0.1096 5.4402 0.0197
precalc   Gone 1 -0.3940 0.1056 13.9103 0.0002
ethnic Asian Fail 1 1.2577 0.7364 2.9167 0.0877
ethnic Asian Gone 1 -0.0889 0.5286 0.0283 0.8664
ethnic Eastern European Fail 1 0.9881 0.7732 1.6332 0.2013
ethnic Eastern European Gone 1 -0.4835 0.5994 0.6505 0.4199
ethnic European not Eastern Fail 1 0.5549 0.6851 0.6559 0.4180
ethnic European not Eastern Gone 1 -0.6811 0.4849 1.9734 0.1601
ethnic Middle-Eastern and Pakistani Fail 1 1.3451 0.7982 2.8401 0.0919
ethnic Middle-Eastern and Pakistani Gone 1 0.0264 0.6123 0.0019 0.9656
ethnic Other and DK Fail 1 0.4595 1.0926 0.1768 0.6741
ethnic Other and DK Gone 1 -1.4702 1.2500 1.3834 0.2395
gender   Fail 1 -0.1684 0.3421 0.2421 0.6227
gender   Gone 1 -0.2690 0.3188 0.7120 0.3988
mtongue   Fail 1 2.1901 0.7748 7.9903 0.0047
mtongue   Gone 1 -0.6472 0.3836 2.8458 0.0916

Odds Ratios

Odds Ratio Estimates
Effect outcome Point Estimate 95% Wald
Confidence Limits
hsgpa Fail 0.889 0.819 0.965
hsgpa Gone 0.912 0.845 0.984
hscalc Fail 0.951 0.919 0.985
hscalc Gone 0.922 0.893 0.952
precalc Fail 0.775 0.625 0.960
precalc Gone 0.674 0.548 0.829
ethnic Asian vs East Indian Fail 3.517 0.831 14.894
ethnic Asian vs East Indian Gone 0.915 0.325 2.578
ethnic Eastern European vs East Indian Fail 2.686 0.590 12.226
ethnic Eastern European vs East Indian Gone 0.617 0.190 1.997
ethnic European not Eastern vs East Indian Fail 1.742 0.455 6.671
ethnic European not Eastern vs East Indian Gone 0.506 0.196 1.309
ethnic Middle-Eastern and Pakistani vs East Indian Fail 3.839 0.803 18.348
ethnic Middle-Eastern and Pakistani vs East Indian Gone 1.027 0.309 3.409
ethnic Other and DK vs East Indian Fail 1.583 0.186 13.476
ethnic Other and DK vs East Indian Gone 0.230 0.020 2.664
gender Fail 0.845 0.432 1.652
gender Gone 0.764 0.409 1.427
mtongue Fail 8.937 1.957 40.802
mtongue Gone 0.524 0.247 1.110

Wald Test for Contrasts

Contrast Test Results
Contrast DF Wald
Chi-Square		 Pr > ChiSq
Demographics 14 25.4777 0.0301
Ethnic and Gender 12 10.0665 0.6101

Prediction of Performance in First-year Calculus

Logistic regression with more than 2 resp. categories

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

Logistic regression with more than 2 resp. categories

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

Logistic regression with more than 2 resp. categories

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

Replicate hsgpa hscalc precalc calc 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='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