Open Access
February 2002 Marginal models for categorical data
Wicher P. Bergsma, Tamás Rudas
Ann. Statist. 30(1): 140-159 (February 2002). DOI: 10.1214/aos/1015362188


Statistical models defined by imposing restrictions on marginal distributions of contingency tables have received considerable attention recently. This paper introduces a general definition of marginal log-linear parameters and describes conditions for a marginal log-linear parameter to be a smooth parameterization of the distribution and to be variation independent. Statistical models defined by imposing affine restrictions on the marginal log-linear parameters are investigated. These models generalize ordinary log-linear and multivariate logistic models. Sufficient conditions for a log-affine marginal model to be nonempty and to be a curved exponential family are given. Standard large-sample theory is shown to apply to maximum likelihood estimation of log-affine marginal models for a variety of sampling procedures.


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Wicher P. Bergsma. Tamás Rudas. "Marginal models for categorical data." Ann. Statist. 30 (1) 140 - 159, February 2002.


Published: February 2002
First available in Project Euclid: 5 March 2002

zbMATH: 1012.62063
MathSciNet: MR1892659
Digital Object Identifier: 10.1214/aos/1015362188

Primary: 62H17
Secondary: 62E99

Keywords: asymptotic normality of maximum likelihood estimates , curved exponential family , existence and connectedness of a model , log-affine and log-linear marginal models , Marginal log-linear parameters , smooth parameterization , variation independence

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 1 • February 2002
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