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

Divergent thinking tests are popular instruments to measure a person's creativity. They often involve scoring fluency, which refers to the count of ideas generated in response to a prompt. The two-parameter Poisson counts model (2PPCM), a generalization of the Rasch Poisson counts model (RPCM) that includes discrimination parameters, has been proposed as a useful approach to analyze fluency scores in creativity tasks, but its estimation was presented in the context of generalized structural equation modeling (GSEM) commercial software (e.g., Mplus). Here, we show how the 2PPCM (and RPCM) can be estimated in a Bayesian multilevel regression framework and interpreted using the R package brms, which provides an interface for the Stan programming language. We illustrate this using an example dataset, which contains fluency scores for three tasks and 202 participants. We discuss model specification, estimation, convergence, fit and comparisons. Furthermore, we provide instructions on plotting item response functions, comparing models, calculating overdispersion and reliability, as well as extracting factor scores.