Yael, Questions like this are better suited for the Statistical Procedures forum. You should start by reading the entire chapter on PROC MIXED. The CLASS statement is for identifying variables that are represented by levels (e.g. race) rather than on a continuium (e.g. age); this is the way that the CLASS statement is used in all of the SAS stat procedures. "Control" variables are another type of independent variable. The SAS procedures don't treat them any differently, but the analyst thinks about them differently. I see the term most often in epidemiology. They are usually independent variables that effect the outcome but aren't the topic of interest in the analysis (e.g. In a general regression framework, someone might want to "examine the effect of BP on heart rate controlling for age."). In MIXED, most control variables are fixed effects.
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