  Multivariate regression techniques are commonly applied to explore the
associations between large numbers of outcomes and predictors. In real-world
applications, the outcomes are often of mixed types, including continuous
measurements, binary indicators, and counts, and the observations may also be
incomplete. Building upon the recent advances in mixed-outcome modeling and
sparse matrix factorization, generalized co-sparse factor regression (GOFAR) is
proposed, which utilizes the flexible vector generalized linear model framework
and encodes the outcome dependency through a sparse singular value
decomposition (SSVD) of the integrated natural parameter matrix. To avoid the
estimation of the notoriously difficult joint SSVD, GOFAR proposes both
sequential and parallel unit-rank estimation procedures. By combining the ideas
of alternating convex search and majorization-minimization, an efficient
algorithm with guaranteed convergence is developed to solve the sparse
unit-rank problem and implemented in the R package gofar. Extensive simulation
studies and two real-world applications demonstrate the effectiveness of the
proposed approach.
