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This study introduces Warp-III bridge sampling for calculating marginal likelihood in hierarchical multinomial processing tree (MPT) models. This method aids in Bayesian model comparison and averaging for cognitive data analysis.

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Area of Science:

  • Cognitive Science
  • Computational Statistics
  • Psychology

Background:

  • Multinomial processing trees (MPTs) are widely used for analyzing categorical data in cognitive research.
  • Hierarchical MPT models often involve numerous parameters, complicating model comparison.
  • Bayesian methods like posterior model probabilities and Bayes factors require marginal likelihood computation.

Purpose of the Study:

  • To present Warp-III bridge sampling as a viable method for computing marginal likelihood in hierarchical MPT models.
  • To demonstrate the practical application of Warp-III using real-world datasets.
  • To highlight the utility of Warp-III in facilitating Bayesian model averaging for MPTs.

Main Methods:

  • Implementation of Warp-III bridge sampling algorithm.
  • Application to hierarchical multinomial processing tree models.
  • Validation using two published cognitive datasets.

Main Results:

  • Warp-III successfully computed the marginal likelihood for hierarchical MPT models.
  • The method proved effective in facilitating Bayesian model averaging.
  • Illustrative examples confirmed the practical utility of the approach.

Conclusions:

  • Warp-III bridge sampling is an effective technique for marginal likelihood estimation in complex hierarchical MPT models.
  • This approach enhances Bayesian inference capabilities for cognitive modeling.
  • The study provides a practical tool for researchers analyzing categorical data with MPTs.