Assumptions

The primary assumptions underlying the analyses performed by PROC GLIMMIX are as follows:

• If the model contains random effects, the distribution of the data conditional on the random effects is known. This distribution is either a member of the exponential family of distributions or one of the supplementary distributions provided by the GLIMMIX procedure. In models without random effects, the unconditional (marginal) distribution is assumed to be known for maximum likelihood estimation, or the first two moments are known in the case of quasi-likelihood estimation.

• The conditional expected value of the data takes the form of a linear mixed model after a monotonic transformation is applied.

• The problem of fitting the GLMM can be cast as a singly or doubly iterative optimization problem. The objective function for the optimization is a function of either the actual log likelihood, an approximation to the log likelihood, or the log likelihood of an approximated model.

For a model containing random effects, the GLIMMIX procedure, by default, estimates the parameters by applying pseudo-likelihood techniques as in Wolfinger and O’Connell (1993) and Breslow and Clayton (1993). In a model without random effects (GLM models), PROC GLIMMIX estimates the parameters by maximum likelihood, restricted maximum likelihood, or quasi-likelihood. See the section Singly or Doubly Iterative Fitting about when the GLIMMIX procedure applies noniterative, singly and doubly iterative algorithms, and the section Default Estimation Techniques about the default estimation methods. You can also fit generalized linear mixed models by maximum likelihood where the marginal distribution is numerically approximated by the Laplace method (METHOD=LAPLACE) or by adaptive Gaussian quadrature (METHOD=QUAD).

Once the parameters have been estimated, you can perform statistical inferences for the fixed effects and covariance parameters of the model. Tests of hypotheses for the fixed effects are based on Wald-type tests and the estimated variance-covariance matrix. The COVTEST statement enables you to perform inferences about covariance parameters based on likelihood ratio tests.

PROC GLIMMIX uses the Output Delivery System (ODS) for displaying and controlling the output from SAS procedures. ODS enables you to convert any of the output from PROC GLIMMIX into a SAS data set. See the section ODS Table Names for more information.

The GLIMMIX procedure uses ODS Graphics to create graphs as part of its output. For general information about ODS Graphics, see Chapter 21, Statistical Graphics Using ODS. For specific information about the statistical graphics available with the GLIMMIX procedure, see the PLOTS options in the PROC GLIMMIX and LSMEANS statements.