  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 paper, 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 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.
