Analysis of Variance for Mixed and Random Effect Models

Just as PROC GLM is the flagship procedure for fixed-effect linear models, the MIXED procedure is the flagship procedure for random- and mixed-effect linear models. PROC MIXED fits a variety of mixed linear models to data and enables you to use these fitted models to make statistical inferences about the data. The default fitting method maximizes the restricted likelihood of the data under the assumption that the data are normally distributed and any missing data are missing at random. This general framework accommodates many common correlated-data methods , including variance component models and repeated measures analyses.

A few other procedures in SAS/STAT software offer limited mixed-linear-model capabilities. PROC GLM fits some random-effects and repeated-measures models, although its methods are based on method-of-moments estimation and a portion of the output applies only to the fixed-effects model. PROC NESTED fits special nested designs and may be useful for large data sets because of its customized algorithms. PROC VARCOMP estimates variance components models, but all of its methods are now available in PROC MIXED. PROC LATTICE fits special balanced lattice designs, but, again, the same models are available in PROC MIXED. In general, PROC MIXED is recommended for nearly all of your linear mixed-model applications.

PROC NLMIXED handles models in which the fixed or random effects enter nonlinearly. It requires that you specify a conditional distribution of the data given the random effects, with available distributions including the normal, binomial, and Poisson. You can alternatively code your own distribution with SAS programming statements. Under a normality assumption for the random effects, PROC NLMIXED performs maximum likelihood estimation via adaptive Gaussian quadrature and a dual quasi-Newton optimization algorithm. Besides standard maximum likelihood results, you can obtain empirical Bayes predictions of the random effects and estimates of arbitrary functions of the parameters with delta-method standard errors. PROC NLMIXED has a wide variety of applications, two of the most common being nonlinear growth curves and overdispersed binomial data.