IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v196y2024ics0167947324000306.html
   My bibliography  Save this article

A mixture of logistic skew-normal multinomial models

Author

Listed:
  • Tu, Wangshu
  • Browne, Ryan
  • Subedi, Sanjeena

Abstract

The logistic normal multinomial distribution is gaining interest in modelling microbiome data. It utilizes a hierarchical structure such that the observed counts conditional on the compositions are assumed to be multinomial random variables and the log-ratio transformed compositions are assumed to be from a Gaussian distribution. While multinomial distribution accounts for the compositional nature of the data, and a Gaussian prior offers flexibility in the structure of covariance matrices, the log-ratio transformed compositions of the microbiome data can be highly skewed, especially at a lower taxonomic level. Thus, a Gaussian distribution may not be an ideal prior for the log-ratio transformed compositions. A novel mixture of logistic skew-normal multinomial (LSNM) distribution is proposed in which a multivariate skew-normal distribution is utilized as a prior for the log-ratio transformed compositions. A variational Gaussian approximation in conjunction with the EM algorithm is utilized for parameter estimation.

Suggested Citation

  • Tu, Wangshu & Browne, Ryan & Subedi, Sanjeena, 2024. "A mixture of logistic skew-normal multinomial models," Computational Statistics & Data Analysis, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:csdana:v:196:y:2024:i:c:s0167947324000306
    DOI: 10.1016/j.csda.2024.107946
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947324000306
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2024.107946?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    2. Shin Yoshimoto & Tze Mun Loo & Koji Atarashi & Hiroaki Kanda & Seidai Sato & Seiichi Oyadomari & Yoichiro Iwakura & Kenshiro Oshima & Hidetoshi Morita & Masahira Hattori & Kenya Honda & Yuichi Ishikaw, 2013. "Obesity-induced gut microbial metabolite promotes liver cancer through senescence secretome," Nature, Nature, vol. 499(7456), pages 97-101, July.
    3. Meredith L. Wallace & Daniel J. Buysse & Anne Germain & Martica H. Hall & Satish Iyengar, 2018. "Variable Selection for Skewed Model-Based Clustering: Application to the Identification of Novel Sleep Phenotypes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 95-110, January.
    4. Nicolas Depraetere & Martina Vandebroek, 2017. "A comparison of variational approximations for fast inference in mixed logit models," Computational Statistics, Springer, vol. 32(1), pages 93-125, March.
    5. Andrew D Fernandes & Jean M Macklaim & Thomas G Linn & Gregor Reid & Gregory B Gloor, 2013. "ANOVA-Like Differential Expression (ALDEx) Analysis for Mixed Population RNA-Seq," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-15, July.
    6. Sanjeena Subedi & Paul McNicholas, 2014. "Variational Bayes approximations for clustering via mixtures of normal inverse Gaussian distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 167-193, June.
    7. Tao Wang & Hongyu Zhao, 2017. "A Dirichlet-tree multinomial regression model for associating dietary nutrients with gut microorganisms," Biometrics, The International Biometric Society, vol. 73(3), pages 792-801, September.
    8. Ian Holmes & Keith Harris & Christopher Quince, 2012. "Dirichlet Multinomial Mixtures: Generative Models for Microbial Metagenomics," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-15, February.
    9. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    10. Azzalini, Adelchi & Browne, Ryan P. & Genton, Marc G. & McNicholas, Paul D., 2016. "On nomenclature for, and the relative merits of, two formulations of skew distributions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 201-206.
    11. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
    12. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    13. R.B. Arellano-Valle & H. Bolfarine & V.H. Lachos, 2007. "Bayesian Inference for Skew-normal Linear Mixed Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(6), pages 663-682.
    14. Sharon Lee & Geoffrey McLachlan, 2013. "On mixtures of skew normal and skew $$t$$ -distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 241-266, September.
    15. Geicho Nakatsu & Xiangchun Li & Haokui Zhou & Jianqiu Sheng & Sunny Hei Wong & William Ka Kai Wu & Siew Chien Ng & Ho Tsoi & Yujuan Dong & Ning Zhang & Yuqi He & Qian Kang & Lei Cao & Kunning Wang & J, 2015. "Gut mucosal microbiome across stages of colorectal carcinogenesis," Nature Communications, Nature, vol. 6(1), pages 1-9, December.
    16. Jingru Zhang & Wei Lin, 2019. "Scalable estimation and regularization for the logistic normal multinomial model," Biometrics, The International Biometric Society, vol. 75(4), pages 1098-1108, December.
    17. Vrbik, Irene & McNicholas, Paul D., 2014. "Parsimonious skew mixture models for model-based clustering and classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 196-210.
    18. Fan Xia & Jun Chen & Wing Kam Fung & Hongzhe Li, 2013. "A Logistic Normal Multinomial Regression Model for Microbiome Compositional Data Analysis," Biometrics, The International Biometric Society, vol. 69(4), pages 1053-1063, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wan-Lun Wang & Luis M. Castro & Yen-Ting Chang & Tsung-I Lin, 2019. "Mixtures of restricted skew-t factor analyzers with common factor loadings," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(2), pages 445-480, June.
    2. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "A mixture of SDB skew-t factor analyzers," Econometrics and Statistics, Elsevier, vol. 3(C), pages 160-168.
    3. Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.
    4. Sharon M. McNicholas & Paul D. McNicholas & Daniel A. Ashlock, 2021. "An Evolutionary Algorithm with Crossover and Mutation for Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 264-279, July.
    5. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Sanjeena Subedi & Paul D. McNicholas, 2021. "A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 89-108, April.
    7. Paula M. Murray & Ryan P. Browne & Paul D. McNicholas, 2020. "Mixtures of Hidden Truncation Hyperbolic Factor Analyzers," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 366-379, July.
    8. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 141-156.
    9. Morris, Katherine & Punzo, Antonio & McNicholas, Paul D. & Browne, Ryan P., 2019. "Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 145-166.
    10. Cristina Tortora & Paul D. McNicholas & Ryan P. Browne, 2016. "A mixture of generalized hyperbolic factor analyzers," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(4), pages 423-440, December.
    11. Redivo, Edoardo & Nguyen, Hien D. & Gupta, Mayetri, 2020. "Bayesian clustering of skewed and multimodal data using geometric skewed normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    12. Marek Śmieja & Magdalena Wiercioch, 2017. "Constrained clustering with a complex cluster structure," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(3), pages 493-518, September.
    13. Yuan Fang & Dimitris Karlis & Sanjeena Subedi, 2022. "Infinite Mixtures of Multivariate Normal-Inverse Gaussian Distributions for Clustering of Skewed Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 510-552, November.
    14. Utkarsh J. Dang & Michael P.B. Gallaugher & Ryan P. Browne & Paul D. McNicholas, 2023. "Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 145-167, April.
    15. Tang, Yang & Browne, Ryan P. & McNicholas, Paul D., 2015. "Model based clustering of high-dimensional binary data," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 84-101.
    16. Sanjeena Subedi & Drew Neish & Stephen Bak & Zeny Feng, 2020. "Cluster analysis of microbiome data by using mixtures of Dirichlet–multinomial regression models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1163-1187, November.
    17. Cristina Tortora & Brian C. Franczak & Ryan P. Browne & Paul D. McNicholas, 2019. "A Mixture of Coalesced Generalized Hyperbolic Distributions," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 26-57, April.
    18. Melnykov, Volodymyr & Zhu, Xuwen, 2018. "On model-based clustering of skewed matrix data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 181-194.
    19. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    20. Patrick LeBlanc & Li Ma, 2023. "Microbiome subcommunity learning with logistic‐tree normal latent Dirichlet allocation," Biometrics, The International Biometric Society, vol. 79(3), pages 2321-2332, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:196:y:2024:i:c:s0167947324000306. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.