  Incomplete covariate vectors are known to be problematic for estimation and
inferences on model parameters, but their impact on prediction performance is
less understood. We develop an imputation-free method that builds on a random
partition model admitting variable-dimension covariates. Cluster-specific
response models further incorporate covariates via linear predictors,
facilitating estimation of smooth prediction surfaces with relatively few
clusters. We exploit marginalization techniques of Gaussian kernels to
analytically project response distributions according to any pattern of missing
covariates, yielding a local regression with internally consistent uncertainty
propagation that utilizes only one set of coefficients per cluster. Aggressive
shrinkage of these coefficients regulates uncertainty due to missing
covariates. The method allows in- and out-of-sample prediction for any
missingness pattern, even if the pattern in a new subject's incomplete
covariate vector was not seen in the training data. We develop an MCMC
algorithm for posterior sampling that improves a computationally expensive
update for latent cluster allocation. Finally, we demonstrate the model's
effectiveness for nonlinear point and density prediction under various
circumstances by comparing with other recent methods for regression of variable
dimensions on synthetic and real data.
