The GLIMMIX Procedure

The GLIMMIX procedure knows two basic modes of parameter estimation, and it can be important for you to understand the differences between the two modes.

In GLM mode, the data are never correlated and there can be no G-side random effects. Typical examples are logistic regression and normal linear models. When you fit a model in GLM mode, the METHOD= option in the PROC GLIMMIX statement has no effect. PROC GLIMMIX estimates the parameters of the model by maximum likelihood, (restricted) maximum likelihood, or quasi-likelihood, depending on the distributional properties of the model (see the section Default Estimation Techniques). The “Model Information” table tells you which estimation method was applied. In GLM mode, the individual observations are considered the sampling units. This has bearing, for example, on how sandwich estimators are computed (see the EMPIRICAL option and the section Empirical Covariance (“Sandwich”) Estimators).

In GLMM mode, the procedure assumes that the model contains random effects or possibly correlated errors, or that the data have a clustered structure. The parameters are then estimated by the techniques specified with the METHOD= option in the PROC GLIMMIX statement.

In general, adding one overdispersion parameter to a generalized linear model does not trigger the GLMM mode. For example, the model defined by the following statements is fit in GLM mode:

proc glimmix;
   model y = x1 x2 / dist=poisson;
   random _residual_;
run;

The parameters of the fixed effects are estimated by maximum likelihood, and the covariance matrix of the fixed-effects parameters is adjusted by the overdispersion parameter.

In a model with uncorrelated data you can trigger the GLMM mode by specifying a SUBJECT= or GROUP= effect in the RANDOM statement. For example, the following statements fit the model by using the residual pseudo-likelihood algorithm:

proc glimmix;
   class id;
   model y = x1 x2 / dist=poisson;
   random _residual_ / subject=id;
run;

If in doubt, you can determine whether a model was fit in GLM mode or GLMM mode. In GLM mode the “Covariance Parameter Estimates” table is not produced. Scale and dispersion parameters in the model appear in the “Parameter Estimates” table.