User Guide

41
Chapter
4
Linear Mixed Models
The Linear Mixed Models procedure expands the general linear model so that the data
are permitted to exhibit correlated and non-constant variability. The mixed linear
model, therefore, provides the flexibility of modeling not only the means of the data
but their variances and covariances as well.
The Linear Mixed Models procedure is also a flexible tool for fitting other models
that can be formulated as mixed linear models. Such models include multilevel
models, hierarchical linear models, and random coefficient models.
Example. A grocery store chain is interested in the effects of various coupons on
customer spending. Taking a random sample of their regular customers, they follow
the spending of each customer for 10 weeks. In each week, a different coupon is
mailed to the customers. Linear Mixed Models is used to estimate the effect of
different coupons on spending while adjusting for correlation due to repeated
observations on each subject over the 10 weeks.
Methods. Maximum likelihood (ML) and restricted maximum likelihood (REML)
estimation.
Statistics. Descriptive statistics: sample sizes, means, and standard deviations of the
dependent variable and covariates for each distinct level combination of the factors.
Factor-level information: sorted values of the levels of each factor and their
frequencies. Also, parameter estimates and confidence intervals for fixed effects, Wald
tests and confidence intervals for parameters of covariance matrices. Type I and Type
III sums of squares can be used to evaluate different hypotheses. Type III is the default.