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.
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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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Reiser, M. Analysis of residuals for the multionmial item response model. Psychometrika 61, 509–528 (1996). https://doi.org/10.1007/BF02294552
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DOI: https://doi.org/10.1007/BF02294552