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Educational and Psychological Measurement
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Evaluating Item Fit for Multidimensional Item Response Models

Bo Zhang

University of Wisconsin-Milwaukee, boz{at}uwm.edu

Clement A. Stone

University of Pittsburgh

This research examines the utility of the s - {chi}2 statistic proposed by Orlando and Thissen (2000) in evaluating item fit for multidimensional item response models. Monte Carlo simulation was conducted to investigate both the Type I error and statistical power of this fit statistic in analyzing two kinds of multidimensional test structures: approximate simple structure and complex structure. Overall, results show that this statistic is capable of evaluating item fit in the application of multidimensional item response models. It is important to identify the structure of multidimensional tests before this fit statistic is applied. For tests with an approximate simple structure, the sampling distribution can be approximated by a standard chi-square distribution. But for tests with a complex structure, that approximation is more complicated. As regards power in detecting the model nonfitting items, the performance of this statistic in multidimensional tests is comparable to that in unidimensional tests.

Key Words: multidimensional item response theory • MIRT • model data fit • item fit • Type I error • power

This version was published on April 1, 2008

Educational and Psychological Measurement, Vol. 68, No. 2, 181-196 (2008)
DOI: 10.1177/0013164407301547
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