Recent technological advances have made it possible to measure multiple types of many features in biomedical studies. However, some data types or features may not be measured for all study subjects because of cost or other constraints. We use a latent variable model to characterize the relationships across and within data types and to infer missing values from observed data. We develop a penalized-likelihood approach for variable selection and parameter estimation and devise an efficient expectation-maximization algorithm to implement our approach. We establish the asymptotic properties of the proposed estimators when the number of features increases at a polynomial rate of the sample size. Finally, we demonstrate the usefulness of the proposed methods using extensive simulation studies and provide an application to a motivating multi-platform genomics study.
Keywords: Adaptive lasso; Factor models; Integrative analysis; Multi-modality data; Multi-platform genomics studies; Penalized regression.