Context-specific independence in graphical log-linear models
This work addresses a methodological bottleneck for statisticians and data analysts working with contingency tables, offering a way to use more expressive models without sacrificing estimation simplicity, though it is incremental in extending existing log-linear frameworks.
The paper tackles the problem of parameter estimation in context-specific graphical log-linear models, which are more expressive but often restricted by decomposability criteria, by introducing a cyclical projection algorithm that obtains maximum likelihood estimates without requiring decomposability, enabling identification of additional context-specific independencies in real data.
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.