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Variational Approximations for Generalized Linear Latent Variable Models

Hui, Francis; Warton, David I.; Ormerod, John T.; Haapaniemi, Viivi; Taskinen, Sara

Description

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...[Show more]

dc.contributor.authorHui, Francis
dc.contributor.authorWarton, David I.
dc.contributor.authorOrmerod, John T.
dc.contributor.authorHaapaniemi, Viivi
dc.contributor.authorTaskinen, Sara
dc.date.accessioned2020-12-20T20:58:28Z
dc.date.available2020-12-20T20:58:28Z
dc.identifier.issn1061-8600
dc.identifier.urihttp://hdl.handle.net/1885/218598
dc.description.abstractGeneralized 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
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherAmerican Statistical Association
dc.sourceJournal of Computational and Graphical Statistics
dc.titleVariational Approximations for Generalized Linear Latent Variable Models
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume26
dc.date.issued2017
local.identifier.absfor080201 - Analysis of Algorithms and Complexity
local.identifier.ariespublicationa383154xPUB5240
local.type.statusPublished Version
local.contributor.affiliationHui, Francis, College of Science, ANU
local.contributor.affiliationWarton, David I., University of New South Wales
local.contributor.affiliationOrmerod, John T., The University of Sydney, School of Mathematics and Statistics
local.contributor.affiliationHaapaniemi, Viivi, Jyvaskylan Yliopisto, Department of Mathematics and Statistics
local.contributor.affiliationTaskinen, Sara, University of Jyvaskyla
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage35
local.bibliographicCitation.lastpage43
local.identifier.doi10.1080/10618600.2016.1164708
dc.date.updated2020-11-23T11:26:16Z
local.identifier.scopusID2-s2.0-85013115744
local.identifier.thomsonID000398004100004
CollectionsANU Research Publications

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