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

Biometrics
Francis K C HuiDavid I Warton

Abstract

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 Ordered Factor LASSO or OFAL penalty for order selection and achieving sparsity in GLLVMs. The OFAL penalty is the first penalty developed specifically for order selection in latent variable models, and achieves this by using a hierarchically structured group LASSO type penalty to shrink entire columns of the loading matrix to zero, while ensuring that non-zero loadings are concentrated on the lower-order factors. Simultaneously, individual element sparsity is achieved through the use of an adaptive LASSO. In conjunction with using an information criterion which promotes aggressive shrinkage, simulation shows that the OFAL penalty performs strongly compared with standard methods and penalties for order selection, achieving sparsity, and prediction in GLLVMs. Applying the OFAL penalty to the Sou...Continue Reading

References

Jan 1, 2012·Statistical Science : a Review Journal of the Institute of Mathematical Statistics·Jian HuangShuangge Ma
Oct 20, 2014·TAG. Theoretical and applied genetics. Theoretische und angewandte Genetik·Alison B SmithBrian R Cullis
Nov 1, 2015·Trends in Ecology & Evolution·David I WartonFrancis K C Hui
Aug 16, 2016·Trends in Ecology & Evolution·David I WartonFrancis K C Hui

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Citations

Jan 29, 2020·Ecology and Evolution·Andrew Hoegh, David W Roberts
Feb 3, 2021·Psychometrika·Christopher J Urban, Daniel J Bauer

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