May, 2007
We consider the problem of joint nonparametric Bayes modeling of predictors and a response variable, with a particular emphasis on functional predictors. Parametric models for the predictor and response are coupled through a joint distribution for subject-specific predictor and response coefficients. This joint distribution is assigned a nonparametric prior, which incorporates Dirichlet process components while allowing the response distribution within predictor clusters to be unknown. Marginalizing out the random atoms and random weights, we obtain a useful closed form bivariate predictor rule. Using this rule, we propose a fast sequential updating and greedy search algorithm for posterior computation. The results are illustrated through simulated data and an application to weight gain during pregnancy and birth weight.
Keywords: Bivariate clustering; Dirichlet process; Functional predictors; Growth mixture model; Joint modeling; Latent class trajectory; Prediction rule.
The manuscript is available in PDF formats.