Generalized co-sparse factor regression

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