Measuring dependence of partition on covariates in cluster analysis

Music City Center 

Mixture models are invaluable tools for density estimation and clustering tasks. After obtaining a partition of responses by the mixture model, assessing the dependence of the partition on covariates is of great importance. This is particularly relevant in applications where understanding the influence of covariates on clusters or subpopulations is crucial, such as in precision medicine for targeted interventions. In this context, we propose the use of the underlap coefficient as a metric for measuring the dependence of estimated partitions on covariates in cluster analysis. Initially designed to quantify separation between distributions, we posit that the underlap coefficient can also serve as an effective complement to posterior predictive checks when using mixture models for clustering purposes. While the posterior predictive check can identify model inadequacies, the underlap offers insights into where to make model adjustments, particularly whether or not to allow weights to depend on covariates. We further propose Bayesian estimators to accurately estimate the underlap coefficient for this task.

Mixture models

Cluster analysis

Covariate dependence

Partition

Underlap coefficient 

Section on Nonparametric Statistics