Within-Item Interactions in Bifactor Models for Ordered-Categorical Item Responses

Recent research in multidimensional item response theory has introduced within-item interaction effects between latent dimensions in the prediction of item responses. The objective of this study was to extend this research to bifactor models to include an interaction effect between the general and specific latent variables measured by an item. Specifically, this research investigates model building approaches to be used when estimating these effects in empirical data and the potential adverse impact of ignoring interaction effects when present in items modeled with the bifactor model. Two simulation studies were conducted with data generated to follow a bifactor 2-parameter normal ogive model and a bifactor graded response model without interaction effects and with varying numbers of items with interaction effects. Model parameters were then estimated from a bifactor model without interactions, with all possible interactions, and with interactions estimated to match the data-generated interactions. The data-generating model was generally favored in relative model comparisons, indexed by deviance information criteria (DIC). Item and respondent parameters were recovered best when the generating model matched the estimated model across all data-generating conditions. Item interaction parameters had small bias, absolute bias, and root mean squared errors decreased with a larger sample size. Regarding model refinement strategies, the highest density intervals and credible intervals correctly identified noninteracting items as not having an interaction at a higher rate compared to interacting items that were generated to have an interaction. A bifactor model with all, none, and reduced interactions was estimated in two empirical data sets with applications in educational measurement and psychological assessment. Results were evaluated in light of the poor performance of the parameter refinement and model comparison strategies investigated in the simulation studies. Implications of this research and future directions of study are discussed