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Analysis of Residuals for the Multinomial Item Response Model

Published online by Cambridge University Press:  01 January 2025

Mark Reiser
Mark Reiser*
Affiliation:
Arizona State University
*
Requests for reprints should be sent to Mark Reiser, Department of Economics, Arizona State University, Tempe, Arizona 85287-3806.
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Abstract

Using the item response model as developed on the multinomial distribution, asymptotic variances are obtained for residuals associated with response patterns and first-, and second-order marginal frequencies of manifest variables. When the model does not fit well, an examination of these residuals may reveal the source of the poor fit. Finally, a limited-information test of fit for the model is developed by using residuals defined for the first-, and second-order marginals. Model evaluation based on residuals for these marginals is particularly useful when the response pattern frequencies are sparse.

Keywords

asymptotic standard errorlatent traitlimited informationfactor analysis
Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 3 , September 1996 , pp. 509 - 528
Copyright
Copyright © 1996 The Psychometric Society

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Footnotes

The author would like to thank Yasuo Amemiya and Joseph Lucke for helpful suggestions. This research was supported by a Research Incentive Grant from Arizona State University.

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