A More Flexible Bayesian Multilevel Bifactor Item Response Theory Model

Multilevel bifactor item response theory (IRT) models are commonly used to account for features of the data that are related to the sampling and measurement processes used to gather those data. These models conventionally make assumptions about the portions of the data structure that represent these features. Unfortunately, when data violate these models' assumptions but these models are used anyway, incorrect conclusions about the cluster effects could be made and potentially relevant dimensions could go undetected. To address the limitations of these conventional models, a more flexible multilevel bifactor IRT model that does not make these assumptions is presented, and this model is based on the generalized partial credit model. Details of a simulation study demonstrating this model outperforming competing models and showing the consequences of using conventional multilevel bifactor IRT models to analyze data that violate these models' assumptions are reported. Additionally, the model's usefulness is illustrated through the analysis of the Program for International Student Assessment data related to interest in science.