Multinomial Logistic Regression 3 or more groups Students

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 Groups Valid Case Processing Summary Marginal N Percentage Poor Good Stay 68 85 103 256 26. 6% 33. 2% 40. 2% 100. 0%

Model Fitting Information Model Fitting Criteria Model -2 Log Likelihood Intercept Only 555. 273 Final 473. 253 Likelihood Ratio Tests Chi-Square df Sig. 82. 020 20 . 000

Pseudo R-Square Cox and Snell . 274 Nagelkerke . 310 Mc. Fadden . 148

Likelihood Ratio Tests Effect Intercept ZMSAT ZVSAT ZHSGPA ZALEKS ZLOC ZNEOOpen ZNEOC ZNEOE ZNEOA ZNEON Model Fitting Criteria -2 Log Likelihood of Reduced Model 488. 053 480. 010 475. 947 493. 748 482. 546 475. 350 473. 641 488. 933 473. 844 473. 951 475. 236 Likelihood Ratio Tests Chi-Square 14. 800 6. 757 2. 694 20. 495 9. 292 2. 096. 388 15. 680. 591. 698 1. 983 df Sig. 2 2 2 . 001. 034. 260. 000. 010. 351. 824. 000. 744. 705. 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 Poor B Std. Wald Error. 212 12. 034 df Sig. Exp(B) 1 . 001 1. 215 1 . 270 . 780 . 051 1 . 820 . 952 -. 838 . 202 17. 161 1 . 000 . 433 ZALEKS -. 619 . 208 8. 833 1 . 003 . 538 ZLOC -. 087 . 211 . 172 1 . 678 . 916 . 125 . 204 . 373 1 . 541 1. 133 . 230 12. 298 1 . 000 . 446 Intercept -. 734 ZMSAT -. 249 . 226 ZVSAT -. 049 . 217 ZHSGPA ZNEOOpen ZNEOC -. 807 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 Good B Intercept -. 109 Std. Error. 159 ZMSAT -. 487 ZVSAT Wald df Sig. Exp(B) . 468 1 . 494 . 192 6. 448 1 . 011 . 614 . 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 Predicted Observed Poor Good Percent Correct Stay Poor 44 12 12 64. 7% Good 18 34 33 40. 0% Stay 12 19 72 69. 9% 28. 9% 25. 4% 45. 7% 58. 6% Overall Percentage

REGWQ A Posteriori Pairwise Comparisons Between Group Means. Group Variable Conscientiousness HS GPA ALEKS Math SAT Persisting 33. 23 A 3. 21 A 59. 82 A 583. 30 A LGS 32. 24 A 3. 14 A 52. 34 B 554. 00 B LPS 28. 21 B 2. 94 B 46. 28 B 552. 79 B Note: Within each column, means sharing a superscript are not significantly different from each other. N = 256.

Presenting the Results • Please see the associated document.