Marginal log-linear parameterization of conditional independence models

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...

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Bibliographic Details
Published in:Biometrika 2010-12, Vol.97 (4), p.1006-1012
Main Authors: RUDAS, TAMÁS, BERGSMA, WICHER P., NÉMETH, RENÁTA
Format: Article
Language:English
Subjects:
Applications
Biology, psychology, social sciences
Chain graph
Conditional independence
Conditional probabilities
Data models
Degrees of freedom
Distribution theory
Estimating techniques
Exact sciences and technology
General topics
Graph theory
Graphical model
Induction assumption
Marginal model
Markov analysis
Markov chains
Markov models
Markov processes
Mathematical models
Mathematics
Maximum likelihood method
Miscellanea
Multilevel models
Parameter estimation
Parameterization
Parametric models
Probability and statistics
Probability distributions
Probability theory and stochastic processes
Sciences and techniques of general use
Smoothness
Statistical analysis
Statistics
Studies
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Summary: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.
ISSN:0006-3444
1464-3510
1464-3510
0006-3444
DOI:10.1093/biomet/asq037