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A Simple Method for Comparing Complex Models: Bayesian Model Comparison for Hierarchical Multinomial Processing Tree
Quentin F Gronau1, Eric-Jan Wagenmakers2, Daniel W Heck3
1University of Amsterdam, Nieuwe Achtergracht 129 B, 1018 WT , Amsterdam, The Netherlands. Quentin.F.Gronau@gmail.com.
Abstract:
Multinomial processing trees (MPTs) are a popular class of cognitive models for categorical data. Typically, researchers compare several MPTs, each equipped with many parameters, especially when the models are implemented in a hierarchical framework. A Bayesian solution is to compute posterior model probabilities and Bayes factors. Both quantities, however, rely on the marginal likelihood, a high-dimensional integral that cannot be evaluated analytically. In this case study, we show how Warp-III bridge sampling can be used to compute the marginal likelihood for hierarchical MPTs. We illustrate the procedure with two published data sets and demonstrate how Warp-III facilitates Bayesian model averaging.
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