@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}
}
