Exploring dependence between categorical variables : benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms
Date
06/2016Keywords
Metadata
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Abstract
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.
Citation
Papathomas , M & Richardson , S 2016 , ' Exploring dependence between categorical variables : benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms ' , Journal of Statistical Planning and Inference , vol. 173 , pp. 47-63 . https://doi.org/10.1016/j.jspi.2016.01.002
Publication
Journal of Statistical Planning and Inference
Status
Peer reviewed
ISSN
0378-3758Type
Journal article
Rights
© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Description
This work was supported by MRC grant G1002319.Collections
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