Marginal Models for Categorial Data

W.P. Bergsma, T. Rudas

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.
Original language English 140-159 The Annals of Statistics 30 1 Published - 2002

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Marginal Model
Statistical Model
Curved Exponential Family
Large Sample Theory
Restriction
Logistic Model
Multivariate Models
Contingency Table
Marginal Distribution
Maximum Likelihood Estimation
Parameterization
Generalise
Sufficient Conditions
Statistical model

Cite this

Bergsma, W. P., & Rudas, T. (2002). Marginal Models for Categorial Data. The Annals of Statistics, 30(1), 140-159.
Bergsma, W.P. ; Rudas, T. / Marginal Models for Categorial Data. In: The Annals of Statistics. 2002 ; Vol. 30, No. 1. pp. 140-159.
title = "Marginal Models for Categorial Data",
abstract = "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.",
author = "W.P. Bergsma and T. Rudas",
year = "2002",
language = "English",
volume = "30",
pages = "140--159",
journal = "The Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
number = "1",

}

Bergsma, WP & Rudas, T 2002, 'Marginal Models for Categorial Data', The Annals of Statistics, vol. 30, no. 1, pp. 140-159.

Marginal Models for Categorial Data. / Bergsma, W.P.; Rudas, T.

In: The Annals of Statistics, Vol. 30, No. 1, 2002, p. 140-159.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Marginal Models for Categorial Data

AU - Bergsma, W.P.

AU - Rudas, T.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

M3 - Article

VL - 30

SP - 140

EP - 159

JO - The Annals of Statistics

JF - The Annals of Statistics

SN - 0090-5364

IS - 1

ER -

Bergsma WP, Rudas T. Marginal Models for Categorial Data. The Annals of Statistics. 2002;30(1):140-159.