A generative approach to modeling data with quantitative and qualitative responses

In many scientific areas, data with mixed 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 fitting QQ responses. Hence in this work, we propose a novel generative approach to jointly model the QQ responses by incorporating the dependency information of predictors. The proposed method is computationally efficient and provides accurate parameter estimation under a penalized likelihood framework. Moreover, because of the generative approach framework, the asymptotically theoretical results of the proposed method are established under some regularity conditions. The performance of the proposed method is examined through simulations and real case studies in material science and genetics.