Results: mathlogreg1.sas

Prediction of Performance in First-year Calculus

Course by passed with proc freq

The FREQ Procedure

The Freq Procedure

Table course2 * passed

Cross-Tabular Freq Table

Frequency
Row Pct
Table of course2 by passed
course2 passed(Passed the course)
No Yes Total
1
44
74.58
15
25.42
59
 
2
149
39.95
224
60.05
373
 
3
8
20.51
31
79.49
39
 
Total
201
270
471
Frequency Missing = 108

Statistics for Table of course2 by passed

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 2 33.5096 <.0001
Likelihood Ratio Chi-Square 2 34.4171 <.0001
Mantel-Haenszel Chi-Square 1 31.6717 <.0001
Phi Coefficient   0.2667  
Contingency Coefficient   0.2577  
Cramer's V   0.2667  

Sample Size = 471
Frequency Missing = 108

WARNING: 19% of the data are missing.

Prediction of Performance in First-year Calculus

Course by passed with dummy vars: Compare LR Chisq = 34.4171

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.MATHEX  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 471

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 201
2 Yes 270

Probability modeled is passed='Yes'.

Note:108 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 644.800 614.383
SC 648.955 626.847
-2 Log L 642.800 608.383

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 34.4171 2 <.0001
Score 33.5096 2 <.0001
Wald 29.2854 2 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 0.4077 0.1057 14.8733 0.0001
c1 1 -1.4838 0.3171 21.8931 <.0001
c3 1 0.9468 0.4104 5.3226 0.0211

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
c1 0.227 0.122 0.422
c3 2.578 1.153 5.762

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 29.2 Somers' D 0.215
Percent Discordant 7.6 Gamma 0.585
Percent Tied 63.2 Tau-a 0.106
Pairs 54270 c 0.608

Test Statement Results

Linear Hypotheses Testing Results
Label Wald
Chi-Square		 DF Pr > ChiSq
course 29.2854 2 <.0001
Course1_vs_2 21.8931 1 <.0001
Course1_vs_3 23.9536 1 <.0001
Course2_vs_3 5.3226 1 0.0211

Prediction of Performance in First-year Calculus

Estimate prob. of passing for for course=3: Compare 31/39 = 0.7949

The IML Procedure

probpass

  probpass
Estimated probability of passing course 3 (Elite) is 0.7948643

Prediction of Performance in First-year Calculus

Use the class and contrast statements

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.MATHEX  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 471

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 201
2 Yes 270

Probability modeled is passed='Yes'.

Note:108 observations were deleted due to missing values for the response or explanatory variables.

Class Level Information

Class Level Information
Class Value Design Variables
course2 1 1 0
  2 0 1
  3 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 644.800 614.383
SC 648.955 626.847
-2 Log L 642.800 608.383

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 34.4171 2 <.0001
Score 33.5096 2 <.0001
Wald 29.2854 2 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
course2 2 29.2854 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter   DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept   1 1.3545 0.3966 11.6673 0.0006
course2 1 1 -2.4307 0.4966 23.9536 <.0001
course2 2 1 -0.9468 0.4104 5.3226 0.0211

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
course2 1 vs 3 0.088 0.033 0.233
course2 2 vs 3 0.388 0.174 0.867

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 29.2 Somers' D 0.215
Percent Discordant 7.6 Gamma 0.585
Percent Tied 63.2 Tau-a 0.106
Pairs 54270 c 0.608

Wald Test for Contrasts

Contrast Test Results
Contrast DF Wald
Chi-Square		 Pr > ChiSq
Catch-up vs Mainstream 1 23.9536 <.0001
Elite vs Mainstream 1 5.3226 0.0211
Catch-up vs Elite 1 21.8931 <.0001

Prediction of Performance in First-year Calculus

Course controlling for score on diagnostic test

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.MATHEX  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 471

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 201
2 Yes 270

Probability modeled is passed='Yes'.

Note:108 observations were deleted due to missing values for the response or explanatory variables.

Class Level Information

Class Level Information
Class Value Design Variables
course2 1 1 0
  2 0 1
  3 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 644.800 546.901
SC 648.955 563.520
-2 Log L 642.800 538.901

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 103.8994 3 <.0001
Score 91.9165 3 <.0001
Wald 75.1047 3 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
course2 2 6.7687 0.0339
totscore 1 54.6730 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter   DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept   1 -1.0462 0.5160 4.1115 0.0426
course2 1 1 -1.3445 0.5393 6.2161 0.0127
course2 2 1 -0.6399 0.4416 2.0998 0.1473
totscore   1 0.2735 0.0370 54.6730 <.0001

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
course2 1 vs 3 0.261 0.091 0.750
course2 2 vs 3 0.527 0.222 1.253
totscore 1.315 1.223 1.413

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 73.6 Somers' D 0.520
Percent Discordant 21.6 Gamma 0.547
Percent Tied 4.9 Tau-a 0.255
Pairs 54270 c 0.760

Wald Test for Contrasts

Contrast Test Results
Contrast DF Wald
Chi-Square		 Pr > ChiSq
Course controlling for totscore 2 6.7687 0.0339

Prediction of Performance in First-year Calculus

What are the ods table names?

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.MATHEX  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 471

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 201
2 Yes 270

Probability modeled is passed='Yes'.

Note:108 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 644.800 546.901
SC 648.955 563.520
-2 Log L 642.800 538.901

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 103.8994 3 <.0001
Score 91.9165 3 <.0001
Wald 75.1047 3 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -1.6861 0.2938 32.9322 <.0001
c1 1 -0.7046 0.3444 4.1874 0.0407
c3 1 0.6399 0.4416 2.0998 0.1473
totscore 1 0.2735 0.0370 54.6730 <.0001

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
c1 0.494 0.252 0.971
c3 1.896 0.798 4.506
totscore 1.315 1.223 1.413

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 73.6 Somers' D 0.520
Percent Discordant 21.6 Gamma 0.547
Percent Tied 4.9 Tau-a 0.255
Pairs 54270 c 0.760

Prediction of Performance in First-year Calculus

Save parameter estimates using ods

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.MATHEX  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 471

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 201
2 Yes 270

Probability modeled is passed='Yes'.

Note:108 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 644.800 546.901
SC 648.955 563.520
-2 Log L 642.800 538.901

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 103.8994 3 <.0001
Score 91.9165 3 <.0001
Wald 75.1047 3 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -1.6861 0.2938 32.9322 <.0001
c1 1 -0.7046 0.3444 4.1874 0.0407
c3 1 0.6399 0.4416 2.0998 0.1473
totscore 1 0.2735 0.0370 54.6730 <.0001

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
c1 0.494 0.252 0.971
c3 1.896 0.798 4.506
totscore 1.315 1.223 1.413

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 73.6 Somers' D 0.520
Percent Discordant 21.6 Gamma 0.547
Percent Tied 4.9 Tau-a 0.255
Pairs 54270 c 0.760

Prediction of Performance in First-year Calculus

Save parameter estimates using ods

The Print Procedure

Data Set WORK.ESTIMOUT

Obs Variable DF Estimate StdErr WaldChiSq ProbChiSq _ESTTYPE_
1 Intercept 1 -1.6861 0.2938 32.9322 <.0001 MLE
2 c1 1 -0.7046 0.3444 4.1874 0.0407 MLE
3 c3 1 0.6399 0.4416 2.0998 0.1473 MLE
4 totscore 1 0.2735 0.0370 54.6730 <.0001 MLE

Prediction of Performance in First-year Calculus

Estimated Probabilty of Passing

The IML Procedure

_LIT1002

Estimated regression coefficients

b

b
-1.686114
-0.70465
0.6398726
0.273462

pihat1

  pihat1
Student in the catch-up class who got 10 right out of 20 0.5851267

Pihat2

  Pihat2
Student in the elite class who got 20 right out of 20 0.988144