@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:000241551800014,
	title = {On the asymptotic distribution of Pearson{\textquoteright}s $X^2$ in cross-validation samples},
	journal = {Psychometrika},
	volume = {71},
	number = {3},
	year = {2006},
	month = {SEP},
	pages = {587-592},
	publisher = {Springer},
	type = {Article},
	abstract = {In categorical data analysis, two-sample cross-validation is used not only for model selection but also to obtain a realistic impression of the overall predictive effectiveness of the model. The latter is of particular importance in the case of highly parametrized models capable of capturing every idiosyncracy of the calibrating sample. We show that for maximum likelihood estimators or other asymptotically efficient estimators Pearson{\textquoteright}s X-2 is not asymptotically chi-square in the two-sample cross-validation framework due to extra variability induced by using different samples for estimation and goodness-off-it testing. We propose an alternative test statistic, X-xval(2) , obtained as a modification of X-2 which is asymptotically chi-square with C-1 degrees of freedom in cross-validation samples. Stochastically, X-xval(2) <= X-2. Furthermore, the use of X-2 instead of X-xval(2) with a chi(2)(C-1) reference distribution may provide an unduly poor impression of fit of the model in the cross-validation sample.},
	keywords = {contingency tables, goodness-of-fit, item response theory modeling, latent class analysis, quadratic form statistics},
	issn = {0033-3123},
	doi = {10.1007/s11336-005-1284-z},
	author = {Joe, Harry and Maydeu-Olivares, Albert}
}
