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

correlation parameter (estimated at 0.5370 in the output) and a variance parameter
(estimated at 0.9709 in the output). The AR1 correlation parameter using PROC
GENMOD was estimated at 0.5254 (slightly different form 0.5370 with PROC GLIM-
MIX). PROC GLIMMIX provides F test statistics (or equivalent T statistics) rather
than chi-square Wald chi-square statistics for the parameter estimates in the default
output. The CHISQ option in the MODEL statement will additionally add chi-square
test statistics in the output.

The output from PROC GLIMMIX uses the terminology R-side parameters for
covariance parameters of the residual matrix (R matrix) and G-side parameters for
the covariance parameters of the random effects (G matrix).

The next example demonstrates how to run a model containing a random intercept
for each subject. The model, shown below, assumes an R matrix with independent
correlation structure and a scalar (1
1) G matrix:

logit PðOUTCOME¼ 1 jXÞ¼ðb 0 þb 0 iÞþb 1 BIRTHWGTþb 2 GENDER

þb 3 DIARRHEA

whereb 0 irepresents the randomeffect for subject

iand is normallydistributed withmean¼ 0

and variance¼ss^2 ,i:e:;b 0 iNð 0 ;ss^2 Þ

The code to run this model in PROC GLIMMIX follows:

PROC GLIMMIX DATA=REF.INFANT;

CLASS IDNO;

MODEL OUTCOME¼BIRTHWGT GENDER DIARRHEA / DIST¼BIN LINK¼LOGIT SOLUTION;

RANDOM INTERCEPT / SUBJECT¼ IDNO;

RANDOM _RESIDUAL_;

RUN;

The first RANDOM statement is followed by the key word INTERCEPT. The SUB-
JECT¼option specifies the variable IDNO as the cluster variable. The second
RANDOM statement (RANDOM RESIDUAL) is optional and requests variance
estimates for the residual in the output but also provides parameter estimates identi-
cal to those provided by the SAS macro called GLIMMIX (a precursor of the GLIM-
MIX procedure). The output is omitted.

The next model includes a random slope for the variable DIARRHEA in addition to
the random intercept. The model is stated as follows:

logit PðOUTCOME¼ 1 jXÞ¼ðb 0 þb 0 iÞþb 1 BIRTHWGTþb 2 GENDER

þðb 3 þb 3 iÞDIARRHEA

whereb 0 irepresents the random intercept for

subjecti,and whereb 3 irepresents a random

slope with the variable DIARRHEA

for subjecti,b 0 iNð 0 ;ss^2 Þandb 3 iNð 0 ;sD^2 Þ

SAS 631