Brian S. Everitt A Handbook of Statistical Analyses using SPSS

it is the parameters reflecting the effects of covariates on the average
response that will be of most interest. Although the parameters modeling
the covariance structure of the observations will not, in general, be of
prime interest (they are often regarded as so-called nuisance parameters),
specifying the wrong model for the covariance structure can affect the
results that are of concern. Diggle (1988), for example, suggests that
overparameterization of the covariance model component (i.e., using too
many parameters for this part of the model) and too restrictive a specification
(too few parameters to do justice to the actual covariance structure
in the data) may both invalidate inferences about the mean response
profiles when the assumed covariance structure does not hold. Consequently,
an investigator has to take seriously the need to investigate each
of the two components of the chosen model. (The univariate analysis of
variance approach to the analysis of repeated measures data described in
Chapter 7 suffers from being too restrictive about the likely structure of
the correlations in a longitudinal data set, and the multivariate option from
overparameterization.)
Everitt and Pickles (2000) give full technical details of a variety of the
models now available for the analysis of longitudinal data. Here we
concentrate on one of these, the linear mixed effects model or random
effects model. Parameters in these models are estimated by maximum
likelihood or by a technique know as restricted maximum likelihood.
Details of the latter and of how the two estimation procedures differ are
given in Everitt and Pickles (2000).
Random effects models formalize the sensible idea that an individual’s
pattern of responses in a study is likely to depend on many characteristics
of that individual, including some that are unobserved. These unobserved
or unmeasured characteristics of the individuals in the study put them at
varying predispositions for a positive or negative treatment response. The
unobserved characteristics are then included in the model as random
variables, i.e., random effects. The essential feature of a random effects
model for longitudinal data is that there is natural heterogeneity across
individuals in their responses over time and that this heterogeneity can
be represented by an appropriate probability distribution. Correlation
among observations from the same individual arises from sharing unobserved
variables, for example, an increased propensity to the condition
under investigation, or perhaps a predisposition to exaggerate symptoms.
Conditional on the values of these random effects, the repeated measurements
of the response variable are assumed to be independent, the so-called
local independence assumption.
A number of simple random effects models are described briefly in
Box 8.1.
© 2004 by Chapman & Hall/CRC Press LLC