The Annals of Statistics

Marginal models for categorical data

Wicher P. Bergsma and Tamás Rudas

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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.

Article information

Ann. Statist., Volume 30, Number 1 (2002), 140-159.

First available in Project Euclid: 5 March 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H17: Contingency tables
Secondary: 62E99: None of the above, but in this section

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


Bergsma, Wicher P.; Rudas, Tamás. Marginal models for categorical data. Ann. Statist. 30 (2002), no. 1, 140--159. doi:10.1214/aos/1015362188.

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