Bayesian Analysis of Repeated Measures Experiments in R

In marketing repeated measures designs have often been overlooked as an appropriate experimental methodology in favor of more popular between-subject designs. Yet, there appears to be a recent surge in interest in repeated measures designs based on a recognition of their advantages in lab and field experiments, which include that they are sensitive to individual differences in the response to experimental treatments and offer advantages for assessing causal mechanisms of mediating variables, even at the individual level. This paper introduces a Bayesian approach to the Analysis of Variance (BANOVA) of repeated measures data derived from mixed within-between subjects experiments with (Normal and) non-Normal dependent variables. We outline some of the key advantages of taking a Bayesian approach to analyzing experimental data. Then we provide details on BANOVA, which incudes the calculation of effect sizes, planned comparisons, spotlight and floodlight analyses. We describe a novel framework for a wide range of mediation, moderation, and moderated mediation analyses. A free software package programmed in R implements these analyses. The package is illustrated through applications to a number of data sets from previously published studies.