  The design of experiments in psychology can often be summarized to
participants reacting to stimuli. For such an experiment, the mixed effects
model with crossed random effects is usually the appropriate tool to analyse
the data because it considers the sampling of both participants and stimuli.
However, these models let to users several choices when analysing data and this
practice may be disruptive for researchers trained to a set of standardized
analysis such as ANOVA. In the present article, we are focusing on the choice
of the correlation structure of the data, because it is both subtle and
influential on the results of the analysis. We provide an overview of several
correlation structures used in the literature and we propose a new one that is
the natural extension of the repeated measures ANOVA. A large simulation study
shows that correlation structures that are either too simple or too complex
fail to deliver credible results, even for designs with only three variables.
We also show how the design of the experiment influences the correlation
structure of the data. Moreover, we provide R code to estimate all the
correlation structures presented in this article, as well as functions
implemented in an R package to compute our new proposal.
