Variational Approximations for Generalized Linear Latent Variable Models
Hui, F. K. C., Warton, D. I., Ormerod, J. T., Haapaniemi, V., & Taskinen, S. (2017). Variational Approximations for Generalized Linear Latent Variable Models. Journal of Computational and Graphical Statistics, 26 (1), 35-43. doi:10.1080/10618600.2016.1164708
Published inJournal of Computational and Graphical Statistics
© 2017 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. This is a final draft version of an article whose final and definitive form has been published by American Statistical Association. Published in this repository with the kind permission of the publisher.
Generalized linear latent variable models (GLLVMs) are a powerful class of models for understanding the relationships among multiple, correlated responses. Estimation, however, presents a major challenge, as the marginal likelihood does not possess a closed form for nonnormal responses. We propose a variational approximation (VA) method for estimating GLLVMs. For the common cases of binary, ordinal, and overdispersed count data, we derive fully closed-form approximations to the marginal log-likelihood function in each case. Compared to other methods such as the expectation-maximization algorithm, estimation using VA is fast and straightforward to implement. Predictions of the latent variables and associated uncertainty estimates are also obtained as part of the estimation process. Simulations show that VA estimation performs similar to or better than some currently available methods, both at predicting the latent variables and estimating their corresponding coefficients. They also show that VA estimation offers dramatic reductions in computation time particularly if the number of correlated responses is large relative to the number of observational units. We apply the variational approach to two datasets, estimating GLLVMs to understanding the patterns of variation in youth gratitude and for constructing ordination plots in bird abundance data. R code for performing VA estimation of GLLVMs is available online. Supplementary materials for this article are available online. ...