Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Ordinal Logistic Regression

A. PROC LOGISTIC

Ordinal logistic regression is demonstrated using the proportional odds model.
Either PROC LOGISTIC or PROC GENMOD can be used to run a proportional
odds model. We continue to use the cancer dataset to demonstrate this model, with
the variable GRADE as the response variable. The model is stated as follows:

ln

PðGRADEgjXÞ

PðGRADE<gjXÞ



¼agþb 1 RACEþb 2 ESTROGEN whereg¼ 1 ; 2

The code using PROC LOGISTIC follows:

PROC LOGISTIC DATA¼REF.CANCER DESCENDING;

MODEL GRADE¼RACE ESTROGEN;

RUN;

The PROC LOGISTIC output for the proportional odds model follows:

The LOGISTIC Procedure

Model Information

Data Set REF.CANCER

Response Variable grade

Number of Response Levels 3

Number of Observations 286

Link Function Logit

Optimization Technique Fisher's scoring

Response Profile

Ordered

Value Grade

Total

Frequency

1253

2 1 105

3 0 128

Score Test for the Proportional Odds

Assumption

Chi-Square DF Pr>ChiSq

0.9051 2 0.6360

Analysis of Maximum Likelihood Estimates

Parameter DF Estimate Standard Error Chi-Square Pr>ChiSq

Intercept 1 1.2744 0.2286 31.0748 <.0001

Intercept2 1 0.5107 0.2147 5.6555 0.0174

620 Appendix: Computer Programs for Logistic Regression