Context-specific independence in graphical log-linear models

Henrik Nyman (), Johan Pensar, Timo Koski and Jukka Corander
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Henrik Nyman: Åbo Akademi University
Johan Pensar: Åbo Akademi University
Timo Koski: KTH Royal Institute of Technology
Jukka Corander: University of Helsinki

Computational Statistics, 2016, vol. 31, issue 4, No 13, 1493-1512

Abstract: Abstract Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific independence. However, parameter estimation is often simpler under a direct parameterization, provided that the model enjoys certain decomposability properties. Here we introduce a cyclical projection algorithm for obtaining maximum likelihood estimates of log-linear parameters under an arbitrary context-specific graphical log-linear model, which needs not satisfy criteria of decomposability. We illustrate that lifting the restriction of decomposability makes the models more expressive, such that additional context-specific independencies embedded in real data can be identified. It is also shown how a context-specific graphical model can correspond to a non-hierarchical log-linear parameterization with a concise interpretation. This observation can pave way to further development of non-hierarchical log-linear models, which have been largely neglected due to their believed lack of interpretability.

Keywords: Graphical model; Context-specific interaction model; Log-linear model; Parameter estimation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00180-015-0606-6

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