Latent variable models have been widely used for modeling the dependence structure of multiple outcomes data. As the formulation of a latent variable model is often unknown a priori, misspecification could distort the dependence structure and lead to unreliable model inference. More- over, the multiple outcomes are often of varying types (e.g., continuous and ordinal), which presents analytical challenges. In this article, we present a class of general latent variable models that can accommodate mixed types of outcomes, and further propose a novel selection approach that simultaneously selects latent variables and estimates model parameters. We show that the proposed estimators are consistent, asymptotically normal, and have the Oracle property. The practical utility of the methods is confirmed via simulations as well as an application to the analysis of a dataset collected in the World Values Survey (WVS), a global research project that explores peoples' values and beliefs and what social and personal characteristics might influence them.



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