Identifying the Source of Misfit in Item Response Theory Models

Multivariate Behavioral Research
Yang Liu, Alberto Maydeu-Olivares

Abstract

When an item response theory model fails to fit adequately, the items for which the model provides a good fit and those for which it does not must be determined. To this end, we compare the performance of several fit statistics for item pairs with known asymptotic distributions under maximum likelihood estimation of the item parameters: (a) a mean and variance adjustment to bivariate Pearson's X(2), (b) a bivariate subtable analog to Reiser's (1996) overall goodness-of-fit test, (c) a z statistic for the bivariate residual cross product, and (d) Maydeu-Olivares and Joe's (2006) M2 statistic applied to bivariate subtables. The unadjusted Pearson's X(2) with heuristically determined degrees of freedom is also included in the comparison. For binary and ordinal data, our simulation results suggest that the z statistic has the best Type I error and power behavior among all the statistics under investigation when the observed information matrix is used in its computation. However, if one has to use the cross-product information, the mean and variance adjusted X(2) is recommended. We illustrate the use of pairwise fit statistics in 2 real-data examples and discuss possible extensions of the current research in various directions.

References

May 20, 2006·The British Journal of Mathematical and Statistical Psychology·Li CaiDavid Thissen
Nov 1, 2007·The British Journal of Mathematical and Statistical Psychology·Li Cai
Jan 23, 2008·The British Journal of Mathematical and Statistical Psychology·Xiaofeng Steven Liu
Sep 2, 2009·Psychological Methods·Carlos G Forero, Alberto Maydeu-Olivares
Jun 27, 2012·Behavior Research Methods·Anna Brown, Alberto Maydeu-Olivares
Jul 1, 2001·Multivariate Behavioral Research·K G Jöreskog, I Moustaki
Jul 1, 2014·Multivariate Behavioral Research·Alberto Maydeu-Olivares, Harry Joe

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Citations

Jan 16, 2016·Psychometrika·Yang Liu, Jan Hannig
Mar 7, 2018·The British Journal of Mathematical and Statistical Psychology·Yanlou LiuWei Tian
Mar 22, 2019·Psychometrika·Yang LiuAlberto Maydeu-Olivares
Dec 19, 2018·Applied Psychological Measurement·Xue ZhangJian Tao
Mar 3, 2020·Frontiers in Psychology·Jochen Ranger, Sören Much

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