The effects on parameter estimation of correlated dimensions and a distribution-restricted trait in a multidimensional item response model

Abstract

This study was designed to assess the effects on parameter estimation of correlated dimensions and a distribution-restricted trait on one dimension using a two-dimensional item response theory model. Multidimensional analysis of simulated two-dimensional item response data fitting a multidimensional two-parameter logistic item response theory model (McKinley & Reckase, 1983a; Reckase & McKinley, 1991) was done using the program MIRTE (Carlson, 1987). Six datasets (2 trait distributions x 3 levels of correlation between dimensions) of 2,000 trait vectors over 104 items were generated. Each dataset was analyzed and replicated 100 times. Trait and item parameters generally were recovered adequately in the datasets in which both traits were normally distributed over the full range. In the datasets with a restricted range of trait level on the second dimension, recovery of the trait and item parameters was affected adversely. The results indicated that MIRTE recovers the structure of a multidimensional correlated space better than reported in earlier studies, especially when items are multidimensional. Index terms: correlated traits, multidimensional item parameter estimates, multidimensional item response theory, multidimensional trait estimates, restricted traits.