Latent Poisson count models for action count data from technology-enhanced assessments

Recent advances in computerized assessments have enabled the use of innovative item formats (e.g., drag-and-drop, scenario-based), necessitating a flexible model that can capture systematic influence of item types on action counts. In this study, we present a refinement scheme that can explicitly model common features of items and allows inference on the item-type effects. We apply multifaceted parameterization to characterize the common and unique features of items and implement the formulation in two existing models, the Rasch and Conway-Maxwell-Poisson count models. The inference procedures for the proposed models are presented using Stan and validated for estimation accuracy. Numerical experimentation with simulated data suggest that the proposed inferential scheme adequately recovers the underlying model parameters. Empirical application demonstrated that the proposed refinement holds practical relevance when data exhibit distinct item-type effects. Based on the findings from the empirical investigation, we discuss practical considerations in applying the Poisson models for analysing count data.