Marginal log-linear parameterization of conditional independence models

• 成果类型: Article
• 署名作者: Rudas, Tamas; Bergsma, Wicher P.; Nemeth, Renata
• 署名单位: Eotvos Lorand University; University of London; London School Economics & Political Science
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq037
• 发表日期: 2010
• 页码: 10061012
• 关键词: markov properties; distributions; joint

摘要

Models defined by a set of conditional independence restrictions play an important role in statistical theory and applications, especially, but not only, in graphical modelling. In this paper we identify a subclass of these consisting of hierarchical marginal log-linear models, as defined by Bergsma & Rudas (2002a). Such models are smooth, which implies the applicability of standard asymptotic theory and simplifies interpretation. Furthermore, we give a marginal log-linear parameterization and a minimal specification of the models in the subclass, which implies the applicability of standard methods to compute maximum likelihood estimates and simplifies the calculation of the degrees of freedom of chi-squared statistics to test goodness-of-fit. The utility of the results is illustrated by applying them to block-recursive Markov models associated with chain graphs.