Models with Subjects and Groups

The concept of a subject as a unit of clustering observations in a mixed model has been described in the preceding section. This concept is important for mixed modeling with the GLIMMIX, HPMIXED, MIXED, and NLMIXED procedures. Observations from two subjects are considered uncorrelated in the analysis. Observations from the same subject are potentially correlated, depending on your specification of the covariance structure. Random effects at the subject level always lead to correlation in the marginal distribution of the observations that belong to the subject.

The GLIMMIX, HPMIXED, and MIXED procedures also support the notion of a GROUP= effect in the specification of the covariance structure. Like a subject effect, a G-side group effect identifies independent random effects. In addition to a subject effect, the group effect assumes that the realizations of the random effects correspond to draws from different distributions; in other words, each level of the group effect is associated with a different set of covariance parameters. For example, the following statements in any of these procedures fit a random coefficient model with fixed intercept and slope and subject-specific random intercept and slope:

class id;
model y = x;
random intercept x / subject=id;

The interpretation of the RANDOM statement is that for each ID an independent draw is made from a bivariate normal distribution with zero mean and a diagonal covariance matrix. In the following statements (in any of these procedures) these independent draws come from different bivariate normal distributions depending on the value of the grp variable.

class id grp;
model y = x;
random intercept x / subject=id group=grp;

Adding GROUP= effects in your model increases the flexibility to model heterogeneity in the covariance parameters, but it can add numerical complexity to the estimation process.