IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0236067.html
   My bibliography  Save this article

Variable selection in multivariate multiple regression

Author

Listed:
  • Asokan Mulayath Variyath
  • Anita Brobbey

Abstract

Introduction: In many practical situations, we are interested in the effect of covariates on correlated multiple responses. In this paper, we focus on estimation and variable selection in multi-response multiple regression models. Correlation among the response variables must be modeled for valid inference. Method: We used an extension of the generalized estimating equation (GEE) methodology to simultaneously analyze binary, count, and continuous outcomes with nonlinear functions. Variable selection plays an important role in modeling correlated responses because of the large number of model parameters that must be estimated. We propose a penalized-likelihood approach based on the extended GEEs for simultaneous parameter estimation and variable selection. Results and conclusions: We conducted a series of Monte Carlo simulations to investigate the performance of our method, considering different sample sizes and numbers of response variables. The results showed that our method works well compared to treating the responses as uncorrelated. We recommend using an unstructured correlation model with the Bayesian information criterion (BIC) to select the tuning parameters. We demonstrated our method using data from a concrete slump test.

Suggested Citation

  • Asokan Mulayath Variyath & Anita Brobbey, 2020. "Variable selection in multivariate multiple regression," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-15, July.
  • Handle: RePEc:plo:pone00:0236067
    DOI: 10.1371/journal.pone.0236067
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0236067
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0236067&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0236067?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
    ---><---

    References listed on IDEAS

    as
    1. You-Gan Wang, 2003. "Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance," Biometrika, Biometrika Trust, vol. 90(1), pages 29-41, March.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Bengt Muthén & Kerby Shedden, 1999. "Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm," Biometrics, The International Biometric Society, vol. 55(2), pages 463-469, June.
    4. Leo Breiman & Jerome H. Friedman, 1997. "Predicting Multivariate Responses in Multiple Linear Regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 3-54.
    5. Amatya, Anup & Demirtas, Hakan, 2015. "OrdNor: An R Package for Concurrent Generation of Correlated Ordinal and Normal Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(c02).
    6. Mary Dupuis Sammel & Louise M. Ryan & Julie M. Legler, 1997. "Latent Variable Models for Mixed Discrete and Continuous Outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 667-678.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bojana Vidović & Bojana Đuričić & Marina Odalović & Andrijana Milošević Georgiev & Ivana Tadić, 2022. "Dietary Supplements Use among Serbian Undergraduate Students of Different Academic Fields," IJERPH, MDPI, vol. 19(17), pages 1-12, September.

    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. Feng, Sanying & Lian, Heng & Xue, Liugen, 2016. "A new nested Cholesky decomposition and estimation for the covariance matrix of bivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 98-109.
    2. Leila Amiri & Mojtaba Khazaei & Mojtaba Ganjali, 2018. "A mixture latent variable model for modeling mixed data in heterogeneous populations and its applications," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(1), pages 95-115, January.
    3. Qiang Sun & Hongtu Zhu & Yufeng Liu & Joseph G. Ibrahim, 2015. "SPReM: Sparse Projection Regression Model For High-Dimensional Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 289-302, March.
    4. Liya Fu & Zhuoran Yang & Fengjing Cai & You-Gan Wang, 2021. "Efficient and doubly-robust methods for variable selection and parameter estimation in longitudinal data analysis," Computational Statistics, Springer, vol. 36(2), pages 781-804, June.
    5. Fokoué, Ernest, 2005. "Mixtures of factor analyzers: an extension with covariates," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 370-384, August.
    6. Lee, Wonyul & Liu, Yufeng, 2012. "Simultaneous multiple response regression and inverse covariance matrix estimation via penalized Gaussian maximum likelihood," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 241-255.
    7. Zehua Chen & Yiwei Jiang, 2020. "A two-stage sequential conditional selection approach to sparse high-dimensional multivariate regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 65-90, February.
    8. Kangning Wang & Xiaofei Sun, 2020. "Efficient parameter estimation and variable selection in partial linear varying coefficient quantile regression model with longitudinal data," Statistical Papers, Springer, vol. 61(3), pages 967-995, June.
    9. Huang, Chao & Farewell, Daniel & Pan, Jianxin, 2017. "A calibration method for non-positive definite covariance matrix in multivariate data analysis," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 45-52.
    10. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    11. Marco Guerra & Francesca Bassi & José G. Dias, 2020. "A Multiple-Indicator Latent Growth Mixture Model to Track Courses with Low-Quality Teaching," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 147(2), pages 361-381, January.
    12. Paul Hewson & Keming Yu, 2008. "Quantile regression for binary performance indicators," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(5), pages 401-418, September.
    13. Guan, Wei & Gray, Alexander, 2013. "Sparse high-dimensional fractional-norm support vector machine via DC programming," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 136-148.
    14. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    15. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    16. Xu, Yang & Zhao, Shishun & Hu, Tao & Sun, Jianguo, 2021. "Variable selection for generalized odds rate mixture cure models with interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    17. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Emmanouil Androulakis & Christos Koukouvinos & Kalliopi Mylona & Filia Vonta, 2010. "A real survival analysis application via variable selection methods for Cox's proportional hazards model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(8), pages 1399-1406.
    19. Meng An & Haixiang Zhang, 2023. "High-Dimensional Mediation Analysis for Time-to-Event Outcomes with Additive Hazards Model," Mathematics, MDPI, vol. 11(24), pages 1-11, December.
    20. Singh, Rakhi & Stufken, John, 2024. "Factor selection in screening experiments by aggregation over random models," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0236067. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.