Marginal models for categorical data

• 成果类型: Article
• 署名作者: Bergsma, WP; Rudas, T
• 署名单位: Tilburg University; HUN-REN; HUN-REN Centre for Social Sciences; Institute for Sociology - HAS; Eotvos Lorand University; Central European University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2002
• 页码: 140-159
• 关键词: log-linear models; maximum-likelihood methods; contingency-tables; regression-models; MULTIVARIATE; association; responses; variables; SUBJECT

摘要

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.