A product partition model with regression on covariates

Peter Müller, Fernando Quintana, Gary L. Rosner

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a probability model for random partitions in the presence of covariates. In other words, we develop a model-based clustering algorithm that exploits available covariates. The motivating application is predicting time to progression for patients in a breast cancer trial. We proceed by reporting a weighted average of the responses of clusters of earlier patients. The weights should be determined by the similarity of the new patient's covariate with the covariates of patients in each cluster. We achieve the desired inference by defining a random partition model that includes a regression on covariates. Patients with similar covariates are a priori more likely to be clustered together. Posterior predictive inference in this model formalizes the desired prediction. We build on product partition models (PPM). We define an extension of the PPM to include a regression on covariates by including in the cohesion function a new factor that increases the probability of experimental units with similar covariates to be included in the same cluster. We discuss implementations suitable for any combination of continuous, categorical, count, and ordinal covariates. An implementation of the proposed model as R-package is available for download.

Original languageEnglish (US)
Pages (from-to)260-278
Number of pages19
JournalJournal of Computational and Graphical Statistics
Volume20
Issue number1
DOIs
StatePublished - Mar 2011

Keywords

  • Clustering
  • Nonparametric Bayes
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

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