A general family of limited information goodness-of-fit statistics for multinomial data

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A general family of limited information goodness-of-fit statistics for multinomial data

TitleA general family of limited information goodness-of-fit statistics for multinomial data
Publication TypeMiscellaneous
Year of Publication2010
AuthorsJoe, H, Maydeu-Olivares, A
Secondary AuthorsKurowicka, D, Joe, H
Keywordscategorical data analysis, cell-focusing, discrete data, item response theory, overdispersion, overlapping cells, Poisson models, quadratic form statistics, Rasch models, score test, sparse contingency tables, zero-inflation
AbstractMaydeu-Olivares and Joe (J. Am. Stat. Assoc. 100:1009-1020, 2005; Psychometrika 71:713-732, 2006) introduced classes of chi-square tests for (sparse) multidimensional multinomial data based on low-order marginal proportions. Our extension provides general conditions under which quadratic forms in linear functions of cell residuals are asymptotically chi-square. The new statistics need not be based on margins, and can be used for one-dimensional multinomials. We also provide theory that explains why limited information statistics have good power, regardless of sparseness. We show how quadratic-form statistics can be constructed that are more powerful than X (2) and yet, have approximate chi-square null distribution in finite samples with large models. Examples with models for truncated count data and binary item response data are used to illustrate the theory.
URL{http://www.worldscibooks.com/economics/7699.html doi = 10.1142/9789814299886, @InCollectionCooke.Joe.ea2011
DOI10.1007/s11336-010-9165-5