# Context-specific independence in graphical log-linear models

A1 Journal article (refereed)

Internal Authors/Editors

Publication Details

List of Authors: Henrik Nyman, Johan Pensar, Timo Koski, Jukka Corander

Publication year: 2015

Journal: Computational Statistics

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 loglinear

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 contextspecific

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.

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.