Order selection and sparsity in latent variable models via the ordered factor LASSO

Summary Generalized linear latent variable models (GLLVMs) offer a general framework for flexibly analyzing data involving multiple responses. When fitting such models, two of the major challenges are selecting the order, that is, the number of factors, and an appropriate structure for the loading matrix, typically a sparse structure. Motivated by the application of GLLVMs to study marine species assemblages in the Southern Ocean, we propose the...