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ERIC Number: EJ895487
Record Type: Journal
Publication Date: 2010-Sep
Pages: 27
Abstractor: As Provided
Reference Count: 34
ISSN: ISSN-0033-3123
A General Family of Limited Information Goodness-of-Fit Statistics for Multinomial Data
Joe, Harry; Maydeu-Olivares, Alberto
Psychometrika, v75 n3 p393-419 Sep 2010
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[squared]" 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.
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A