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Multifactorial Dimensionality Reduction for Disordered Trait

We develop our recent works concerning the identification of the factors associated with a certain complex disease. The case of disordered discrete trait is studied. We build two models (3D and 2D) for the range of response variable indicating the state of the health of a patient. In this work we consider the problem of optimal forecast for response variable depending on a finite collection of factors with values in arbitrary finite set. The quality of prediction is described by the error function involving a penalty function. The estimation of the error requires some cross-validation procedure. The developed approach provides the basis to identify the set of significant factors. Such problem arises naturally, e.g., in the genome-wide association study. Using simulated data we illustrate the efficiency of our method.