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 m...
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Oxford University Press (OUP)
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Online Access: | http://dx.doi.org/10.1111/biom.12888 https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fbiom.12888 https://onlinelibrary.wiley.com/doi/pdf/10.1111/biom.12888 https://onlinelibrary.wiley.com/doi/full-xml/10.1111/biom.12888 https://academic.oup.com/biometrics/article-pdf/74/4/1311/55805281/biometrics_74_4_1311.pdf |
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croxfordunivpr:10.1111/biom.12888 2024-05-12T08:11:28+00:00 Order Selection and Sparsity in Latent Variable Models via the Ordered Factor LASSO Hui, Francis K. C. Tanaka, Emi Warton, David I. 2018 http://dx.doi.org/10.1111/biom.12888 https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fbiom.12888 https://onlinelibrary.wiley.com/doi/pdf/10.1111/biom.12888 https://onlinelibrary.wiley.com/doi/full-xml/10.1111/biom.12888 https://academic.oup.com/biometrics/article-pdf/74/4/1311/55805281/biometrics_74_4_1311.pdf en eng Oxford University Press (OUP) https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model http://onlinelibrary.wiley.com/termsAndConditions#vor Biometrics volume 74, issue 4, page 1311-1319 ISSN 0006-341X 1541-0420 Applied Mathematics General Agricultural and Biological Sciences General Immunology and Microbiology General Biochemistry, Genetics and Molecular Biology General Medicine Statistics and Probability journal-article 2018 croxfordunivpr https://doi.org/10.1111/biom.12888 2024-04-18T08:16:55Z 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 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 Southern Ocean marine species dataset suggests the available environmental predictors explain roughly half of the total covariation between species, thus leading to a smaller number of latent variables and increased sparsity in the loading matrix compared to a model without any covariates. Article in Journal/Newspaper Southern Ocean Oxford University Press Southern Ocean Biometrics 74 4 1311 1319 |
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Oxford University Press |
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croxfordunivpr |
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English |
topic |
Applied Mathematics General Agricultural and Biological Sciences General Immunology and Microbiology General Biochemistry, Genetics and Molecular Biology General Medicine Statistics and Probability |
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Applied Mathematics General Agricultural and Biological Sciences General Immunology and Microbiology General Biochemistry, Genetics and Molecular Biology General Medicine Statistics and Probability Hui, Francis K. C. Tanaka, Emi Warton, David I. Order Selection and Sparsity in Latent Variable Models via the Ordered Factor LASSO |
topic_facet |
Applied Mathematics General Agricultural and Biological Sciences General Immunology and Microbiology General Biochemistry, Genetics and Molecular Biology General Medicine Statistics and Probability |
description |
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 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 Southern Ocean marine species dataset suggests the available environmental predictors explain roughly half of the total covariation between species, thus leading to a smaller number of latent variables and increased sparsity in the loading matrix compared to a model without any covariates. |
format |
Article in Journal/Newspaper |
author |
Hui, Francis K. C. Tanaka, Emi Warton, David I. |
author_facet |
Hui, Francis K. C. Tanaka, Emi Warton, David I. |
author_sort |
Hui, Francis K. C. |
title |
Order Selection and Sparsity in Latent Variable Models via the Ordered Factor LASSO |
title_short |
Order Selection and Sparsity in Latent Variable Models via the Ordered Factor LASSO |
title_full |
Order Selection and Sparsity in Latent Variable Models via the Ordered Factor LASSO |
title_fullStr |
Order Selection and Sparsity in Latent Variable Models via the Ordered Factor LASSO |
title_full_unstemmed |
Order Selection and Sparsity in Latent Variable Models via the Ordered Factor LASSO |
title_sort |
order selection and sparsity in latent variable models via the ordered factor lasso |
publisher |
Oxford University Press (OUP) |
publishDate |
2018 |
url |
http://dx.doi.org/10.1111/biom.12888 https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fbiom.12888 https://onlinelibrary.wiley.com/doi/pdf/10.1111/biom.12888 https://onlinelibrary.wiley.com/doi/full-xml/10.1111/biom.12888 https://academic.oup.com/biometrics/article-pdf/74/4/1311/55805281/biometrics_74_4_1311.pdf |
geographic |
Southern Ocean |
geographic_facet |
Southern Ocean |
genre |
Southern Ocean |
genre_facet |
Southern Ocean |
op_source |
Biometrics volume 74, issue 4, page 1311-1319 ISSN 0006-341X 1541-0420 |
op_rights |
https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model http://onlinelibrary.wiley.com/termsAndConditions#vor |
op_doi |
https://doi.org/10.1111/biom.12888 |
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Biometrics |
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74 |
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4 |
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1311 |
op_container_end_page |
1319 |
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1798855198950555648 |