The Multiplicative Mixed Model with the mumm R package as a General and Easy Random Interaction Model Tool

Abstract: Multiplicative mixed models can be applied in a wide range of scientific disciplines, since they are relevant in every situation where an interaction between a fixed effect and a random effect is present. Until now, no R package has been published, which can fit this type of models. The lack of user-friendly open source tools to fit these models, is the main reason that the models are not used as often as they could or should be. In this paper we introduce the user-friendly R package $\mathsf{mumm}$ for fitting multiplicative mixed models in a time-efficient manner. To illustrate the interpretation of the multiplicative term, we provide four data analysis examples, where the model is fitted to data sets that stem from studies in sensometrics, agriculture and medicine. With these examples it is shown that the statistical inference can be improved by using a multiplicative mixed model, instead of a linear mixed model which is usually employed.