Abstract
Multinomial processing tree (MPT) models allow testing hypotheses on latent psychological processes that underlie human behavior. However, past applications of this model class have mainly been restricted to the analysis of main effects. In this paper, we adopt the interaction concept as defined in log-linear models and show why it is appropriate for MPT models. We then explain how to implement and test ordinal and disordinal two-way interaction hypotheses in MPT models. We also show how our method generalizes to higher-order interactions involving three or more factors. An empirical example from source memory and aging demonstrates the applicability of this method and allows for directly testing the associative deficit theory that age differences are larger in associative (e.g., source) memory as opposed to item memory. Throughout the paper, we explain how most analytic steps can be easily implemented in the freely available software multiTree.
Highlights
Psychologists are typically interested in internal processes that drive behavior but are not directly observable
Only one Multinomial processing tree (MPT) model parameter would be of interest that is estimated in the four cells resulting from fully crossing both condition factors
We illustrate our method to test a prominent theory of cognitive aging that predicts an ordinal two-way interaction of age group and type of memory on memory performance
Summary
Psychologists are typically interested in internal processes (e.g., cognitions and emotions) that drive behavior but are not directly observable. Multinomial processing tree (MPT) models are stochastic models that, based on observable participant responses, allow for estimation of the probabilities of such unobservable processes taking place or not. Almost all applications of MPT models in psychology involve simple parameter comparisons across experimental conditions or groups of participants, testing only main effects on model parameters, arguably because standard MPT parameter tests do not readily allow to test interactions. We explain how MPT models can be reparameterized to allow for testing interaction hypotheses. We provide an easy-to-follow introduction and an application example from cognitive aging on how to implement parameter constraints to test two-way (and higher-order) interaction hypotheses, using the software multiTree (Moshagen, 2010)
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