Limited- and full-information estimation and goodness-of-fit testing in $2^n$ contingency tables: A unified framework

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Limited- and full-information estimation and goodness-of-fit testing in $2^n$ contingency tables: A unified framework

TitleLimited- and full-information estimation and goodness-of-fit testing in $2^n$ contingency tables: A unified framework
Publication TypeJournal Article
Year of Publication2005
AuthorsMaydeu-Olivares, A, Joe, H
JournalJournal of the American Statistical Association
Volume100
Pagination1009-1020
Date PublishedSEP
ISSN0162-1459
AbstractHigh-dimensional contingency tables tend to be sparse, and standard goodness-of-fit statistics such as X-2 cannot be used without pooling categories. As an improvement on arbitrary pooling, for goodness of fit of large 2(n) contingency tables, we propose classes of quadratic form statistics based on the residuals of margins or multivariate moments up to order r. These classes of test statistics are asymptotically chi-squared distributed under the null hypothesis. Further, the marginal residuals are useful for diagnosing lack of fit of parametric models. We show that when r is small (r = 2, 3), the proposed statistics have better small-sample properties and are asymptotically more powerful than X-2 for some useful multivariate binary models. Related to these test statistics is a class of limited-information estimators based on low-dimensional margins. We show that these estimators have high efficiency for one commonly used latent trait model for binary data.
DOI10.1198/016214504000002069