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.
Highlights
Multinomial processing trees (MPTs) are a popular class of cognitive models for categorical data
We show how Warp-III bridge sampling can be used to compute the marginal likelihood for hierarchical MPTs
Current hierarchical MPT approaches, do not incorporate Bayesian model comparison methods based on Bayes factors and posterior model probabilities, possibly because of the computational challenges associated with the evaluation of the marginal likelihood
Summary
Multinomial processing trees (MPTs) are a popular class of cognitive models for categorical data. Updating factor where p(data | Mi ) is the marginal likelihood of model Mi. If model comparison involves assessing the tenability of parameter constraints in a set of nested models, posterior model probabilities can be used to quantify the model-averaged evidence that a parameter is free to vary or should be constrained across different groups or experimental conditions (e.g., Hoeting, Madigan, Raftery, & Volinsky, 1999; Rouder, Morey, Verhagen, Swagman, & Wagenmakers, 2017). Warp-III improves upon simpler bridge sampling techniques (e.g., DiCiccio, Kass, Raftery, & Wasserman, 1997, Gronau et al, 2017) by respecting potential skewness in the posterior distribution—a typical consequence of estimating parameters of cognitive models from scarce data (e.g., Ly et al, 2018; Matzke et al, 2015). The first example focuses on Bayesian model averaging for nested models; the second example focuses on the computation of the Bayes factor for non-nested models
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