Context-specific independence in graphical log-linear models

TL;DR

This paper introduces a cyclical projection algorithm for estimating parameters in context-specific graphical log-linear models, enhancing model expressiveness and interpretability without requiring decomposability.

Contribution

It presents a novel algorithm for maximum likelihood estimation in non-decomposable, context-specific log-linear models, expanding their applicability and interpretability.

Findings

Lifting decomposability increases model expressiveness.

The algorithm effectively estimates parameters in complex models.

Context-specific models can be interpreted through non-hierarchical parameterizations.

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.