Bayesian Estimation of Generalized Log-Linear Poisson Item Response Models for Fluency Scores Using brms and Stan

Area of Science:

• Psychometrics
• Cognitive Psychology
• Statistical Modeling

Background:

• Divergent thinking tests are widely used to assess creativity, often focusing on fluency (idea count).
• The two-parameter Poisson counts model (2PPCM) and Rasch Poisson counts model (RPCM) are suitable for analyzing fluency data.
• Previous estimation of these models relied on commercial generalized structural equation modeling (GSEM) software.

Purpose of the Study:

• To demonstrate the estimation of the 2PPCM and RPCM within a Bayesian multilevel regression framework.
• To provide practical guidance on using the R package brms for analyzing creativity task fluency scores.
• To offer a reproducible and accessible method for psychometric modeling of creativity data.

Main Methods:

• Bayesian multilevel regression modeling using the R package brms, interfacing with the Stan programming language.
• Estimation and interpretation of the two-parameter Poisson counts model (2PPCM) and Rasch Poisson counts model (RPCM).
• Illustration with an example dataset of fluency scores from 202 participants across three tasks.

Main Results:

• Successful estimation of 2PPCM and RPCM models in a Bayesian framework using brms.
• Demonstration of model specification, convergence assessment, and model fit evaluation.
• Provision of practical guidance on plotting item response functions, comparing models, and calculating reliability.

Conclusions:

• Bayesian multilevel regression with brms provides a flexible and accessible alternative for estimating 2PPCM and RPCM models for creativity research.
• This approach facilitates detailed psychometric analysis of divergent thinking fluency data.
• The study offers a valuable resource for researchers seeking to analyze creativity measures using modern statistical techniques.