# Refining Bayesian hierarchical MPT modeling: Integrating prior knowledge and ordinal expectations

## TL;DR

This paper improves Bayesian hierarchical MPT models by integrating prior knowledge and testing ordinal expectations in psychological theories.

## Contribution

The paper introduces refined Bayesian modeling practices for MPT models to better test ordinal and disordinal expectations.

## Key findings

- Default priors in MPT models can lead to nonsensical predictions for individuals and populations.
- Bayesian model comparison using Bayes factors can effectively test ordinal and disordinal interactions.
- The proposed methods were successfully applied to empirical psychological data.

## Abstract

Multinomial processing tree (MPT) models are a broad class of statistical models used to test sophisticated psychological theories. The research questions derived from these theories often go beyond simple condition effects on parameters and involve ordinal expectations (e.g., the same-direction effect on the memory parameter is stronger in one experimental condition than another) or disordinal expectations (e.g., the effect reverses in one experimental condition). Here, we argue that by refining common modeling practices, Bayesian hierarchical models are well suited to estimate and test these expectations. Concretely, we show that the default priors proposed in the literature lead to nonsensical predictions for individuals and the population distribution, leading to problems not only in model comparison but also in parameter estimation. Rather than relying on these priors, we argue that MPT modelers should determine priors that are consistent with their theoretical knowledge. In addition, we demonstrate how Bayesian model comparison may be used to test ordinal and disordinal interactions by means of Bayes factors. We apply the techniques discussed to empirical data from Bell et al. Journal of Experimental Psychology: Learning, Memory, and Cognition, 41, 456–472 (2015).

The online version contains supplementary material available at 10.3758/s13428-024-02370-y.