February 15-18, 2009 Washington State Convention Center Seattle ...

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ANALYSIS OF REPEATED MEASURES DATA – JUST WHAT ARE MIXED MODELS?
Loveday L. Conquest
University of Washington
School of Aquatic & fishery Sciences
1122 NE Boat St.
Seattle WA 98195-5020 USA
conquest@u.washington.edu
Analysis of repeated measures data is a problem often faced by aquaculture scientists. This occurs when each of several subjects
is followed through time. The subjects could be individual organisms, or Petri dishes, or tanks of fish. There is often more
than one treatment being compared. An incorrect analysis is to consider this as a two-way analysis of variance (ANOVA),
with Treatment as one factor, Time as the second factor, and the number of data points in each Treatment x Time combination
as independent “replicates”, upon which the error term is based. However, a simple two-way ANOVA commits the error of
temporal pseudoreplication, as this approach does not take into account the fact that each subject produces a “time trace”. Any
analysis of repeated measures data should specifically incorporate the notion of the time trace. This is precisely what mixed
effects models do, as they provide a statistical model with a correlation structure. The term “mixed effects models” arises from
the fact that they ultimately combine fixed effects (which influence only the mean of the response variable) and random effects
(which influence only the variance of the response variable).
This session will introduce the audience to the use of mixed effects models in analyzing data that involve time traces, where
temporal autocorrelation from repeated measures on the same individuals is expected to occur.