The GLIMMIX Procedure

Parameterization of Generalized Linear Mixed Models

PROC GLIMMIX constructs a generalized linear mixed model according to the specifications in the CLASS, MODEL, and RANDOM statements. Each effect in the MODEL statement generates one or more columns in the matrix $\bX $, and each G-side effect in the RANDOM statement generates one or more columns in the matrix $\bZ $. R-side effects in the RANDOM statement do not generate model matrices; they serve only to index observations within subjects. This section shows how the GLIMMIX procedure builds $\bX $ and $\bZ $. You can output the $\bX $ and $\bZ $ matrices to a SAS data set with the OUTDESIGN= option in the PROC GLIMMIX statement.

The general rules and techniques for parameterization of a linear model are given in GLM Parameterization of Classification Variables and Effects of Chapter 19: Shared Concepts and Topics. The following paragraphs discuss how these rules differ in a mixed model, in particular, how parameterization differs between the $\bX $ and the $\bZ $ matrix.