CHIDIM: A FORTRAN Program for Assessing the Dimensionality of Binary Item Responses Based on Mcdonald's Nonlinear Factor Analytic Model

Abstract

The assumption of unidimensionality is central to most item response theory (IRT) models. Procedures based on McDonald's nonlinear factor analytic model and accompanying principle of weak local independence have proven to be useful with respect to identifying the number of dimensions underlying a set of binary item responses. In particular, an approximate chi-square statistic, which tests the null hypothesis that the off-iagonal elements of a residual correlation matrix are equal to zero after fitting an m-factor model to a set of item responses, was shown to be accurate in identifying the true number of dimensions underlying various simulated test structures. This article briefly describes CHIDIM, a FORTRAN computer program that calculates the approximate chi-square statistic. The use of the program and the interpretation of the results are illustrated through a simulated data set.

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