Nathan Bowling (Committee Member), David Lahuis (Committee Chair), Corey Miller (Committee Member), Scott Watamanuik (Committee Member)
Doctor of Philosophy (PhD)
Despite frequent use of the adjusted chi-square to degrees of freedom ratio (χ2/df) test for Item Response Theory fit (Drasgow, Levine, Tsien, Williams. and Mead, 1995), there remains a lack of empirical testing of the statistic's Type I error rates and power. The present study compared the adjusted χ2/df test to two other commonly used IRT fit statistics. The other fit indices examined were S-χ2 (Orlando and Thissen, 2000) and χ2* (Stone's, 2000). This study also addressed misfit based on the possibility that the item responses analyzed were created based on a different response process than that assumed by the IRT model used to analyze the data. Results suggest that the adjusted χ2/df test without cross validation has the best Type I error rate, is the test least affected by changes in sample size and test length, and is best suited for the detection of misfit based on violations of the local independence assumption. Stone's χ2* however appeared to be the best statistic to detect misfit based on the model misspecification introduced. Furthermore, the power/Type I error rate trade off for the adjusted chi-square to degrees of freedom ratio test demonstrated that the cut off value for acceptable fit of 3.0 may not always be the ideal cut-off value.
Department or Program
Department of Psychology
Year Degree Awarded
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