A General Bayesian Multidimensional Item Response Theory Model for Small and Large Samples

Abstract

Although item response theory (IRT) models such as the bifactor, two-tier, and between-item-dimensionality IRT models have been devised to confirm complex dimensional structures in educational and psychological data, they can be challenging to use in practice. The reason is that these models are multidimensional IRT (MIRT) models and thus are highly parameterized, making them only suitable for data provided by large samples. Unfortunately, many educational and psychological studies are conducted on a small scale, leaving the researchers without the necessary MIRT models to confirm the hypothesized structures in their data. To address the lack of modeling options for these researchers, we present a general Bayesian MIRT model based on adaptive informative priors. Simulations demonstrated that our MIRT model could be used to confirm a two-tier structure (with two general and six specific dimensions), a bifactor structure (with one general and six specific dimensions), and a between-item six-dimensional structure in rating scale data representing sample sizes as small as 100. Although our goal was to provide a general MIRT model suitable for smaller samples, the simulations further revealed that our model was applicable to larger samples. We also analyzed real data from 121 individuals to illustrate that the findings of our simulations are relevant to real situations.