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Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables

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Abstract

We introduce a family of goodness-of-fit statistics for testing composite null hypotheses in multidimensional contingency tables. These statistics are quadratic forms in marginal residuals up to order r. They are asymptotically chi-square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator. For a widely used item response model, when r is small and multidimensional tables are sparse, the proposed statistics have accurate empirical Type I errors, unlike Pearson’s X 2. For this model in nonsparse situations, the proposed statistics are also more powerful than X 2. In addition, the proposed statistics are asymptotically chi-square when applied to subtables, and can be used for a piecewise goodness-of-fit assessment to determine the source of misfit in poorly fitting models.

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Authors and Affiliations

  1. University of Barcelona and Instituto De Empresa Business School, Spain

    Albert Maydeu-Olivares

  2. University of British Columbia, Canada

    Harry Joe

  3. Faculty of Psychology, University of Barcelona, P. Valle de Hebrón, 171, 08035, Barcelona, Spain

    Albert Maydeu-Olivares

Authors
  1. Albert Maydeu-Olivares
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  2. Harry Joe
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Correspondence to Albert Maydeu-Olivares.

Additional information

This research has been supported by the Department of Universities, Research, and Information Society (DURSI) of the Catalan Government, by grant BSO2003-08507 of the Spanish Ministry of Science and Technology, and an NSERC Canada grant. We are grateful to the referees for comments leading to improvements.

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Maydeu-Olivares, A., Joe, H. Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables. Psychometrika 71, 713–732 (2006). https://doi.org/10.1007/s11336-005-1295-9

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  • DOI: https://doi.org/10.1007/s11336-005-1295-9

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