Shared Concepts and Topics

Parameterization of Model Effects

The general form of a linear regression model is defined in Regression Models and Models with Classification Effects: Regression Models and Models with Classification Effects as

\begin{align*}  \bY & = \bX \bbeta + \bepsilon \end{align*}

This section describes how matrices of regressor effects such as $\bX $ are constructed in SAS/STAT software. These constructions (parameterization rules) apply to regression models, models with classification effects, generalized linear models, and mixed models. The simplest and most general parameterization rules are the ones used in the GLM procedure, and they are discussed first. Several procedures also support alternate parameterizations of classification variables, including the CATMOD, GENMOD, GLMSELECT, LOGISTIC, PHREG, SURVEYLOGISTIC, and SURVEYPHREG procedures. These are discussed after the GLM parameterization of classification variables and model effects.

All modeling procedures that have a CLASS statement support classification variables and effects, and those procedures that additionally support the supplemental parameterizations have a PARAM= option in the CLASS statement.