Multi-Unidimensional IRT Model And Its Application

Unidimensional item response theory (IRT) models are useful when each item is designed to measure some facet of a unified latent trait. In practical applications, items are not necessarily measuring the same underlying trait, and hence the more general multiunidimensional model should be considered. At this moment, our concern is facing specific data, how do we determine which model is closer to the real structure for the data or to the actual latent structure. This paper mainly provides several two-parameter normal ogive models with simple structure: unidimensional IRT model, multi-unidimensional IRT model which has been called multidimensional model with simple structure or the between-items multidimensional and constrained multi-unidimensional model. We examines the bayesian estimation of the specific data in the corresponding model, as well as model comparison based on the Bayesian deviance information criterion and posterior prediction model checks (PPMC).