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The VARCOMP Procedure |

On the other hand, an effect is classified as a random effect when you want to make inferences on an entire population, and the levels in your experiment represent only a sample from that population. Psychologists comparing test results between different groups of subjects would consider Subject as a random effect. Depending on the psychologists' particular interest, the Group effect might be either fixed or random. For example, if the groups are based on the sex of the subject, then Sex would be a fixed effect. But if the psychologists are interested in the variability in test scores due to different teachers, then they might choose a random sample of teachers as being representative of the total population of teachers, and Teacher would be a random effect. Note that, in the soybean example presented earlier, if the scientists are interested in making inferences on the entire population of soybean varieties and randomly choose three varieties for testing, then Variety would be a random effect.

If all the effects in a model (except for the intercept) are
considered random effects, then the model is called a *random
effects model*;
likewise, a model with only fixed effects is called a
*fixed-effects model*. The more common case, where some factors
are fixed and others are random, is called a *mixed model*.
In
PROC VARCOMP, by default, effects are assumed to be random. You
specify which effects are fixed by using the FIXED= option in the
MODEL statement. In general, if an interaction or nested effect
contains any effect that is random, then the interaction or nested
effect should be considered as a random effect as well.

In the linear model, each level of a fixed effect contributes a fixed
amount to the expected value of the dependent variable. What makes a
random effect different is that each level of a random effect
contributes an amount that is viewed as a sample from a population of
normally distributed variables, each with mean 0, and an unknown
variance, much like the usual random error term that is a part of all
linear models. The estimate of the variance associated with the
random effect is known as the *variance component*
because it is
measuring the part of the overall variance contributed by that effect.
Thus, PROC VARCOMP estimates the variance of the random variables that
are associated with the random effects in your model, and the variance
components tell you how much each of the random factors contributes to
the overall variability in the dependent variable.

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