A comparison of correlation and regression approaches for multinomial processing tree models

Abstract

Multinomial processing tree (MPT) models are a class of stochastic models for categorical data that have recently been extended to account for heterogeneity in individuals by assuming separate parameters per participant. These extensions enable the estimation of correlations among model parameters and correlations between model parameters and external covariates. The present study compares different approaches regarding their ability to estimate both types of correlations. For parameter–parameter correlations, we considered two Bayesian hierarchical MPT models – the beta-MPT approach and the latent-trait approach – and two frequentist approaches that fit the data of each participant separately, either involving a correction for attenuation or not (corrected and uncorrected individual-model approach). Regarding parameter-covariate correlations, we additionally considered the latent-trait regression. Recovery performance was determined via a Monte Carlo simulation varying sample size, number of items, extent of heterogeneity, and magnitude of the true correlation. The results indicate the smallest bias regarding parameter–parameter​ correlations for the latent-trait approach and the corrected individual-model approach and the smallest bias regarding parameter-covariate correlations for the latent-trait regression and the corrected individual-model approach. However, adequately recovering correlations of MPT parameters generally requires a sufficiently large number of observations and sufficient heterogeneity.