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In many scientific areas, data with quantitative and qualitative (QQ)responses are commonly encountered with a large number of predictors. Byexploring the association between QQ responses, existing approaches oftenconsider a joint model of QQ responses given the predictor variables. However,the dependency among predictive variables also provides useful information formodeling QQ responses. In this work, we propose a generative approach to modelthe joint distribution of the QQ responses and predictors. The proposedgenerative model provides efficient parameter estimation under a penalizedlikelihood framework. It achieves accurate classification for qualitativeresponse and accurate prediction for quantitative response with efficientcomputation. Because of the generative approach framework, the asymptoticoptimality of classification and prediction of the proposed method can beestablished under some regularity conditions. The performance of the proposedmethod is examined through simulations and real case studies in materialscience and genetics.

A Generative Approach to Joint Modeling of Quantitative and Qualitative Responses