Section 9. Random Effects in GLM, MIXED, and NLMIXED

Definition of a Random Effect

Before entering a factor on a RANDOM statement be sure to understand the 
difference between a fixed and a random effect. Fixed effects were defined 
in Section 6, that is, the levels of the factors chosen are the only ones 
of interest.

A factor is considered random when the levels chosen represent a "random" 
selection from a much larger population of equally acceptable levels. The 
definition implies that the chosen "values" are a sample of 
interchangeable individuals or conditions. That is, they represent an 
arbitrary realization from a much larger set of other equally acceptable 
values.

Elements of the design structure, e.g., the blocks in a completely 
randomized block design, are most often treated as random effects. Blocks 
are only a subset of the larger set of blocks over which inference is to 
be made. In repeated measures studies on humans or animals, the individual 
subject is generally treated as a random effect since it is likely the 
researcher could identify other persons or animals which would have been 
acceptable for the study. One assumes there is no interaction among 
elements of the design structure and elements of the treatment structure.


The RANDOM Statement

The syntax for random effects as entered on the RANDOM statements in both 
PROC GLM and PROC MIXED look very much alike other than how the 
specification of random effects appear on the MODEL and RANDOM statements. 
As an example, if one observation is to be obtained from male and female 
subjects (gender) and they are selected from a set of randomly chosen 
sites, the effect of site is likely considered random when many other 
sites are possible. A comparison of the commands for PROCs GLM and MIXED 
indicates one distinct difference:

PROC GLM DATA=ex;                    PROC MIXED DATA=ex TYPE=reml;
CLASS site gender;                   CLASS site gender;
MODEL y = gender site / solution;    MODEL y = gender / solution;
RANDOM site;                         RANDOM site;
RUN;                                 RUN;

Notice that in both procedures the variable names for site and gender 
appear on the CLASS statement. With PROC GLM variables that are treated as 
random effects are placed on both the MODEL and RANDOM statements; in PROC 
MIXED they only appear on the RANDOM statement. The equivalent SPSS random 
effects model is:

MIXED
  y BY site gender
  /FIXED = gender | SSTYPE(3)
  /METHOD = REML
  /PRINT = SOLUTION 
  /RANDOM site | COVTYPE(VC) .




When Should One Treat Variables as Random Effects?

Random effects models work well when the responses are more similar within 
a site than between sites. This indicates a larger between-site variance 
relative to the within-site variance.

Less variation between sites than within sites leads to nonconvergence 
since they may produce negative variance estimates. If that is the 
problem, then specifying NOBOUND on the PROC statement, which might 
achieve convergence.

PROC MIXED DATA=ex TYPE=reml NObound;
Etc..
Run;