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Bergsma, Wicher P.; Rudas, Tamás

Marginal models for categorical data. (English) Zbl 1012.62063

Ann. Stat. 30, No. 1, 140-159 (2002).
Summary: 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.

Cited in 2 Reviews
Cited in 56 Documents

MSC:

62H17 Contingency tables
62J12 Generalized linear models (logistic models)
62E20 Asymptotic distribution theory in statistics

Software:

cmm
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References:

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