Limited and Full Information Estimation and Goodness-of-Fit Testing in 2n Contingency Tables

32 Pages Posted: 14 Oct 2007

See all articles by Harry Joe

Harry Joe

University of British Columbia - Department of Statistics

Alberto Maydeu Olivares

Fundación Instituto de Empresa, S.L.

Date Written: May 2003

Abstract

High-dimensional contingency tables tend to be sparse and standard goodness-of-fit statistics such as X2 cannot be used without pooling categories. As an improvement on arbitrary pooling, for goodness-of-fit of large 2n contingency tables, we propose a class of quadratic form statistics based on the residuals of margins or multivariate moments up to order r. Further, the marginal residuals are useful for diagnosing lack of fit of parametric models. These classes of test statistics are asymptotically chisquare and have better small sample properties than X2. We also show that these classes of test statistics have better power than X2 for some useful multivariate binary models. Related to this class of test statistics is a class of limited information estimators based on low-dimensional margins. We show that these estimators have high efficiency for one commonly used latent trait model for binary data.

Keywords: item response modeling, quadratic form statistics, low-dimensional margins, limited

JEL Classification: C00

Suggested Citation

Joe, Harry and Maydeu Olivares, Alberto, Limited and Full Information Estimation and Goodness-of-Fit Testing in 2n Contingency Tables (May 2003). Instituto de Empresa Business School Working Paper No. WP03-14, Available at SSRN: https://ssrn.com/abstract=1019782 or http://dx.doi.org/10.2139/ssrn.1019782

Harry Joe

University of British Columbia - Department of Statistics ( email )

2329 West Mall
Vancouver, British Columbia BC V6T 1Z2
Canada
(604) 822 2829 (Phone)

Alberto Maydeu Olivares (Contact Author)

Fundación Instituto de Empresa, S.L. ( email )

Mª Molina, 11,13,15
Madrid, Madrid 28006
Spain
915 689 732 (Phone)

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