The GENMOD Procedure

Overview

The GENMOD procedure fits generalized linear models, as defined by Nelder and Wedderburn (1972). The class of generalized linear models is an extension of traditional linear models that allows the mean of a population to depend on a linear predictor through a nonlinear link function and allows the response probability distribution to be any member of an exponential family of distributions. Many widely used statistical models are generalized linear models. These include classical linear models with normal errors, logistic and probit models for binary data, and log-linear models for multinomial data. Many other useful statistical models can be formulated as generalized linear models by the selection of an appropriate link function and response probability distribution. Refer to McCullagh and Nelder (1989) for a discussion of statistical modeling using generalized linear models. The books by Aitkin, Anderson, Francis, and Hinde (1989) and Dobson (1990) are also excellent references with many examples of applications of generalized linear models. Firth (1991) provides an overview of generalized linear models.

The analysis of correlated data arising from repeated measurements when the measurements are assumed to be multivariate normal has been studied extensively. However, the normality assumption may not always be reasonable; for example, different methodology must be used in the data analysis when the responses are discrete and correlated. Generalized Estimating Equations (GEEs) provide a practical method with reasonable statistical efficiency to analyze such data.

Liang and Zeger (1986) introduced GEEs as a method of dealing with correlated data when, except for the correlation among responses, the data can be modeled as a generalized linear model. For example, correlated binary and count data in many cases can be modeled in this way.

The GENMOD procedure can fit models to correlated responses by the GEE method. You can use PROC GENMOD to fit models with most of the correlation structures from Liang and Zeger (1986) using GEEs. Refer to Liang and Zeger (1986), Diggle, Liang, and Zeger (1994), and Lipsitz, Fitzmaurice, Orav, and Laird (1994) for more details on GEEs.

Overview

What is a Generalized Linear Model?

Examples of Generalized Linear Models

The GENMOD Procedure