Comparison of Factor Simplicity Indices for Dichotomous Data: DETECT R,Bentler's Simplicity Index,and the Loading Simplicity Index

A primary assumption underlying several of the common methods for modeling item response data is unidimensionality, that is, test items tap into only one latent trait. This assumption can be assessed several ways, using nonlinear factor analysis and DETECT, a method based on the item conditional covariances. When multidimensionality is identified, a question of interest concerns the degree to which individual items are related to the latent traits. In cases where an item response is primarily associated with one of these traits it is said that (approximate) simple structure exists, whereas when the item response is related to both traits, the structure is complex. This study investigated the performance of three indices designed to assess the underlying structure present in item response data, two of which are based on factor analysis and one on DETECT. Results of the Monte Carlo simulations show that none of the indices works uniformly well in identifying the structure underlying item responses, although the DETECT r-ratio might be promising in differentiating between approximate simple and complex structures under certain circumstances.