@booklet {NSERC Canada; Hong Kong Polytechnic University; University of Saskatchewan},
	title = {A general family of limited information goodness-of-fit statistics for multinomial data},
	journal = {Dependence Modeling: Vine Copula Handbook},
	volume = {75},
	number = {3},
	year = {2010},
	month = {SEP},
	pages = {393-419},
	publisher = {Springer},
	type = {Article},
	chapter = {10},
	address = {Singapore},
	abstract = {Maydeu-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.},
	keywords = {categorical 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},
	issn = {0033-3123},
	doi = {10.1007/s11336-010-9165-5},
	url = {{http://www.worldscibooks.com/economics/7699.html doi = 10.1142/9789814299886,  @InCollectionCooke.Joe.ea2011},
	author = {Joe, Harry and Maydeu-Olivares, Alberto},
	editor = {Kurowicka, D. and Joe, H.}
}
@article { ISI:000245010700005,
	title = {Limited information goodness-of-fit testing in multidimensional contingency tables},
	journal = {Psychometrika},
	volume = {71},
	number = {4},
	year = {2006},
	month = {DEC},
	pages = {713-732},
	publisher = {Springer},
	type = {Article},
	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{\textquoteright}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.},
	keywords = {categorical data analysis, Composite likelihood, item response theory, Lisrel, multivariate discrete data, multivariate multinomial distribution},
	issn = {0033-3123},
	doi = {10.1007/s11336-005-1295-9},
	author = {Maydeu-Olivares, Albert and Joe, Harry}
}
