The Effects on Parameter Estimation of Correlated Dimensions and a Distribution-Restricted Trait in a Multidimensional Item Response Model

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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 multi dimensional 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 distri butions x 3 levels of correlation between dimen sions) of 2,000 trait vectors over 104 items were generated. Each dataset was analyzed and repli cated 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 struc ture of a multidimensional correlated space better than reported in earlier studies, especially when items are multidimensional.