Effect of Noncompensatory Multidimensionality on Separate and Concurrent Estimation in IRT Observed Score Equating

Anton A. Béguin, Citogroup
Bradley A. Hanson, ACT, Inc.

Paper presented at the Annual Meeting of the National Council on Measurement in Education (Seattle, April, 2001)

This paper is available as Citogroup Measurement and Research Department Report 2001-02.

Abstract: In this article, the results of a simulation study comparing the performance of separate and concurrent estimation of a unidimensional item response theory (IRT) model applied to multidimensional noncompensatory data are reported. Data were simulated according to a two-dimensional noncompensatory IRT model for both equivalent and nonequivalent groups designs. The criteria used were the accuracy of estimating a distribution of observed scores, and the accuracy of IRT observed score equating. In general, unidimensional concurrent estimation resulted in lower or equivalent total error than separate estimation, although there were a few cases where separate estimation resulted in slightly less error than concurrent estimation. Estimates from the correctly specified multidimensional model generally resulted in less error than estimates from the unidimensional model. The results of this study, along with results from a previous study where data were simulated using a compensatory multidimensional model, make clear that multidimensionality of the data affects the relative performance of separate and concurrent estimation, although the degree to which the unidimensional model produces biased results with multidimensional data depends on the type of multidimensionality present.

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