Title: Fast and universal estimation of latent variable models using extended variational approximations
Authors: Pekka Korhonen - University of Jyvaskyla (Finland)
Francis Hui - The Australian National University (Australia)
Jenni Niku - University of Jyvaskyla (Finland)
Sara Taskinen - University of Jyvaskyla (Finland) [presenting]
Abstract: Generalized linear latent variable models (GLLVMs) are a class of methods for analyzing multiresponse data. One of the main features of GLLVMs is their capacity to handle a variety of response types (e.g. counts, binomial and (semi-)continuous responses, and proportions data) as well as between response correlations. The inclusion of unobserved latent variables, however, poses a computational challenge, as the resulting marginal likelihood function involves an intractable integral. This has spurred research into approximation methods to overcome this integral, with a recent and particularly computationally scalable one being that of variational approximations (VA). Unfortunately, the closed-form variational lower bounds have only been obtained for certain combinations of response distributions and link functions. We thus propose an extended variational approximations (EVA) approach which widens the set of VA-applicable GLLVMs. In EVA we replace the complete-data likelihood function with its second order Taylor approximation about the mean of the variational distribution and obtain a closed-form approximation to the marginal likelihood for any response type and link function. We use simulation studies to demonstrate that EVA is competitive in terms of estimation and inferential performance relative to VA and a Laplace approximation approach, while being computationally more scalable.