Using recursive partitioning to account for parameter heterogeneity in multinomial processing tree models

In multinomial processing tree (MPT) models, individual differences between the participants in a study lead to heterogeneity of the model parameters. While subject covariates may explain these differences, it is often unknown in advance how the parameters depend on the available covariates, that is, which variables play a role at all, interact, or have a nonlinear influence, etc. Therefore, a new approach for capturing parameter heterogeneity in MPT models is proposed based on the machine learning method MOB for model-based recursive partitioning. This recursively partitions the covariate space, leading to an MPT tree with subgroups that are directly interpretable in terms of effects and interactions of the covariates. The pros and cons of MPT trees as a means of analyzing the effects of covariates in MPT model parameters are discussed based on a simulation experiment as well as on two empirical applications from memory research. Software that implements MPT trees is provided via the mpttree function in the psychotree package in R.