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

Choosing the correlation structure of mixed effect models for experiments with stimuli