  In many applied fields incomplete covariate vectors are commonly encountered.
It is well known that this can be problematic when making inference on model
parameters, but its impact on prediction performance is less understood. We
develop a method based on covariate dependent partition models that seamlessly
handles missing covariates while completely avoiding any type of imputation.
The method we develop allows in-sample predictions as well as out-of-sample
prediction, even if the missing pattern in the new subjects' incomplete
covariate vector was not seen in the training data. Any data type, including
categorical or continuous covariates are permitted. In simulation studies the
proposed method compares favorably. We illustrate the method in two application
examples.
