Limited information goodness-of-fit testing in multidimensional contingency tables

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Limited information goodness-of-fit testing in multidimensional contingency tables

TitleLimited information goodness-of-fit testing in multidimensional contingency tables
Publication TypeJournal Article
Year of Publication2006
AuthorsMaydeu-Olivares, A, Joe, H
JournalPsychometrika
Volume71
Pagination713-732
Date PublishedDEC
Type of ArticleArticle
ISSN0033-3123
Keywordscategorical data analysis, Composite likelihood, item response theory, Lisrel, multivariate discrete data, multivariate multinomial distribution
AbstractWe 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.
DOI10.1007/s11336-005-1295-9