Multinomial Logistic Regression
3 or more groups
• Students in Engineering at ECU
1. Persisters – still in the program after 2 years
2. Left in Good Standing (GPA 2.00)
3. Left in Poor Standing (GPA < 2.00)
Predictor Variables
• SAT Scores (Verbal and Quantitative)• ALEKS Scores – calculus readiness• High School GPA• NEO Five-Factor Inventory (5 variables)• Nowicki–Duke Locus of Control (high =
external)
Standardize Predictors
Analyze, Regression, Multinomial Logistic
Ask for a classification table
Output
Case Processing Summary
NMarginal
Percentage
Groups
Poor 68 26.6%
Good 85 33.2%
Stay 103 40.2%
Valid 256 100.0%
Model Fitting Information
Model
Model Fitting Criteria Likelihood Ratio Tests
-2 Log Likelihood Chi-Square df Sig.
Intercept Only 555.273
Final 473.253 82.020 20 .000
Pseudo R-Square
Cox and Snell .274
Nagelkerke .310
McFadden .148
Likelihood Ratio Tests
Effect
Model Fitting Criteria
Likelihood Ratio Tests
-2 Log Likelihood of Reduced Model Chi-Square df Sig.
Intercept 488.053 14.800 2 .001ZMSAT 480.010 6.757 2 .034ZVSAT 475.947 2.694 2 .260ZHSGPA 493.748 20.495 2 .000ZALEKS 482.546 9.292 2 .010ZLOC 475.350 2.096 2 .351ZNEOOpen 473.641 .388 2 .824ZNEOC 488.933 15.680 2 .000ZNEOE 473.844 .591 2 .744ZNEOA 473.951 .698 2 .705ZNEON 475.236 1.983 2 .371
k-1 sets of coefficients
• Earlier we designated the reference group to be that with the highest code, the persisters.
• Each of the other two groups will be contrasted with that group.
Groupsa B Std. Error
Wald df Sig. Exp(B)
Poor
Intercept -.734 .212 12.034 1 .001
ZMSAT -.249 .226 1.215 1 .270 .780
ZVSAT -.049 .217 .051 1 .820 .952
ZHSGPA -.838 .202 17.161 1 .000 .433
ZALEKS -.619 .208 8.833 1 .003 .538
ZLOC -.087 .211 .172 1 .678 .916
ZNEOOpen .125 .204 .373 1 .541 1.133
ZNEOC -.807 .230 12.298 1 .000 .446
ZNEOE .008 .216 .001 1 .972 1.008
ZNEOA -.030 .207 .022 1 .883 .970
ZNEON -.289 .252 1.314 1 .252 .749
Those who left in poor standing versus those who persisted.
Groupsa B Std. Error
Wald df Sig. Exp(B)
Good
Intercept -.109 .159 .468 1 .494
ZMSAT -.487 .192 6.448 1 .011 .614
ZVSAT .239 .173 1.913 1 .167 1.270
ZHSGPA -.171 .165 1.071 1 .301 .843
ZALEKS -.215 .171 1.573 1 .210 .807
ZLOC .189 .178 1.125 1 .289 1.208
ZNEOOpen .023 .164 .020 1 .888 1.023
ZNEOC -.044 .194 .052 1 .819 .956
ZNEOE .126 .177 .505 1 .477 1.134
ZNEOA -.145 .182 .631 1 .427 .865
ZNEON -.233 .197 1.392 1 .238 .792
Classification
Observed
Predicted
Poor Good StayPercent Correct
Poor 44 12 12 64.7%
Good 18 34 33 40.0%
Stay 12 19 72 69.9%
Overall Percentage 28.9% 25.4% 45.7% 58.6%
REGWQ
Variable
Group Conscientiousness HS GPA ALEKS Math SAT
Persisting 33.23A 3.21A 59.82A 583.30A
LGS 32.24A 3.14A 52.34B 554.00B
LPS 28.21B 2.94B 46.28B 552.79B
Note: Within each column, means sharing a superscript are not significantly different from each other. N = 256.
A Posteriori Pairwise Comparisons Between Group Means.
Presenting the Results
• Please see the associated document.