When two data types (markers and secondary traits) are available, we achieve improved prediction of a binary trait by two steps that are designed to ensure that a significant intrinsic effect of a phenotype is incorporated in the relation before accounting for the effects of genotypes. First, we sparsely regress the secondary traits on the markers and replace the secondary traits by their residuals to obtain the intrinsic effects of phenotype variables with the influence of genotypes removed.
Then, we develop a sparse logistic classifier using the markers and residuals so that the intrinsic phenotypes may be selected first to avoid being overwhelmed by the genotypes due to their numerical advantage. This classifier uses forward selection aided by a penalty term and can be computed effectively by a technique called the one-pass method. It compares favorably with other classifiers on simulated and real data.