User Guide

33
Chapter
3
Variance Components Analysis
The Variance Components procedure, for mixed-effects models, estimates the
contribution of each random effect to the variance of the dependent variable. This
procedure is particularly interesting for analysis of mixed models such as split plot,
univariate repeated measures, and random block designs. By calculating variance
components, you can determine where to focus attention in order to reduce the variance.
Four different methods are available for estimating the variance components:
minimum norm quadratic unbiased estimator (MINQUE), analysis of variance
(ANOVA), maximum likelihood (ML), and restricted maximum likelihood (REML).
Various specifications are available for the different methods.
Default output for all methods includes variance component estimates. If the ML
method or the REML method is used, an asymptotic covariance matrix table is also
displayed. Other available output includes an ANOVA table and expected mean
squares for the ANOVA method, and an iteration history for the ML and REML
methods. The Variance Components procedure is fully compatible with the GLM
Univariate procedure.
WLS Weight allows you to specify a variable used to give observations different
weights for a weighted analysis, perhaps to compensate for different precision of
measurement.
Example. At an agriculture school, weight gains for pigs in six different litters are
measured after one month. The litter variable is a random factor with six levels. (The
six litters studied are a random sample from a large population of pig litters.) The
investigator finds out that the variance in weight gain is attributable to the difference
in litters much more than to the difference in pigs within a litter.