  This manuscript is concerned with relating two approaches that can be used to
explore complex dependence structures between categorical variables, namely
Bayesian partitioning of the covariate space incorporating a variable selection
procedure that highlights the covariates that drive the clustering, and
log-linear modelling with interaction terms. We derive theoretical results on
this relation and discuss if they can be employed to assist log-linear model
determination, demonstrating advantages and limitations with simulated and real
data sets. The main advantage concerns sparse contingency tables. Inferences
from clustering can potentially reduce the number of covariates considered and,
subsequently, the number of competing log-linear models, making the exploration
of the model space feasible. Variable selection within clustering can inform on
marginal independence in general, thus allowing for a more efficient
exploration of the log-linear model space. However, we show that the clustering
structure is not informative on the existence of interactions in a consistent
manner. This work is of interest to those who utilize log-linear models, as
well as practitioners such as epidemiologists that use clustering models to
reduce the dimensionality in the data and to reveal interesting patterns on how
covariates combine.

Methodology