  Motivated by the problem of accurately predicting gap times between
successive blood donations, we present here a general class of Bayesian
nonparametric models for clustering. These models allow for prediction of new
recurrences, accommodating covariate information that describes the personal
characteristics of the sample individuals. We introduce a prior for the random
partition of the sample individuals which encourages two individuals to be
co-clustered if they have similar covariate values. Our prior generalizes PPMx
models in the literature, which are defined in terms of cohesion and similarity
functions. We assume cohesion functions which yield mixtures of PPMx models,
while our similarity functions represent the compactness of a cluster. We show
that including covariate information in the prior specification improves the
posterior predictive performance and helps interpret the estimated clusters, in
terms of covariates in the blood donation application.
