  In many scientific areas, data with quantitative and qualitative (QQ)
responses are commonly encountered with a large number of predictors. By
exploring the association between QQ responses, existing approaches often
consider a joint model of QQ responses given the predictor variables. However,
the dependency among predictive variables also provides useful information for
modeling QQ responses. In this work, we propose a generative approach to model
the joint distribution of the QQ responses and predictors. The proposed
generative model provides efficient parameter estimation under a penalized
likelihood framework. It achieves accurate classification for qualitative
response and accurate prediction for quantitative response with efficient
computation. Because of the generative approach framework, the asymptotic
optimality of classification and prediction of the proposed method can be
established under some regularity conditions. The performance of the proposed
method is examined through simulations and real case studies in material
science and genetics.
