Generalized integrative principal component analysis for multi-type data with block-wise missing structure.

High-dimensional multi-source data are encountered in many fields. Despite recent developments on the integrative dimension reduction of such data, most existing methods cannot easily accommodate data of multiple types (e.g. binary or count-valued). Moreover, multi-source data often have block-wise missing structure, i.e. data in one or more sources may be completely unobserved for a sample. The heterogeneous data types and presence of block-wise missing data pose significant challenges to the integration of multi-source data and further statistical analyses. In this article, we develop a low-rank method, called generalized integrative principal component analysis (GIPCA), for the simultaneous dimension reduction and imputation of multi-source block-wise missing data, where different sources may have different data types. We also devise an adapted Bayesian information criterion (BIC) criterion for rank estimation. Comprehensive simulation studies demonstrate the efficacy of the proposed method in terms of rank estimation, signal recovery, and missing data imputation. We apply GIPCA to a mortality study. We achieve accurate block-wise missing data imputation and identify intriguing latent mortality rate patterns with sociological relevance.