Binary models for marginal independence

doi:10.1111/j.1467-9868.2007.00636.x

Binary models for marginal independence

2008-02-06

47

OA

AI

M

Mathias Drton

T

Thomas S. Richardson *

DOI：10.1111/j.1467-9868.2007.00636.x

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Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach that is taken is graphical and draws on analogies with multivariate Gaussian models for marginal independence. For the graphical model representation we use bidirected graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed by using a version of the iterated conditional fitting algorithm. Finally we consider combining these models with symmetry restrictions.

Keyword:

bidirected graph

covariance graph

graphical Markov model

iterative conditional fitting

maximum likelihood estimation

mobius inversion

Binary models for marginal independence

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