Bayesian estimation of multinomial processing tree models with heterogeneity in participants and items.

Area of Science:

• Statistics
• Cognitive Science
• Psychometrics

Background:

• Multinomial processing tree (MPT) models are established tools for analyzing categorical data.
• Existing MPT models often lack flexibility in accounting for participant and item variability.
• Bayesian latent-trait pair-clustering models offer a robust framework for cognitive modeling.

Purpose of the Study:

• To introduce a crossed-random effects extension of the Bayesian latent-trait pair-clustering MPT model.
• To provide a flexible statistical framework for analyzing categorical data with participant and item heterogeneity.
• To demonstrate the applicability of the proposed model to novel experimental data.

Main Methods:

• The proposed model extends the Bayesian latent-trait pair-clustering MPT model.
• It incorporates crossed-random effects for participants and items, assuming additive effects on the probit scale.
• Multivariate normal distributions are postulated for the random effects, implemented using WinBUGS.

Main Results:

• A novel Bayesian MPT model with crossed-random effects was successfully implemented.
• The model effectively accounts for both participant-specific and item-specific variations.
• The application to experimental data demonstrated the practical utility of the approach.

Conclusions:

• The developed crossed-random effects pair-clustering MPT model provides a powerful extension for categorical data analysis.
• This flexible framework can be adapted to various other MPT models.
• The approach enhances the ability to model complex data structures in cognitive and psychological research.