IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v154y2017icp249-261.html
   My bibliography  Save this article

Density ratio model for multivariate outcomes

Author

Listed:
  • Marchese, Scott
  • Diao, Guoqing

Abstract

The Density Ratio Model is a semi-parametric regression model which allows analysis of data from any exponential family without making a parametric distribution assumption. For univariate outcomes several authors have shown desirable properties of this model including robustness to mis-specification and efficiency of the estimators within a suitable class. In this paper we consider analysis of multivariate outcomes with this model, where each marginal distribution is from an exponential family. We show that the model successfully analyzes data from mixed outcome types (continuous, integer, binary), providing valid tests of the joint effects of covariates. Furthermore, for continuous outcomes we provide a bootstrap technique which correctly estimates the underlying marginal regression parameters and provides appropriate coverage probabilities without specifying the covariance structure. The methods are demonstrated via simulation studies and analysis of healthcare data.

Suggested Citation

  • Marchese, Scott & Diao, Guoqing, 2017. "Density ratio model for multivariate outcomes," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 249-261.
    • Handle: RePEc:eee:jmvana:v:154:y:2017:i:c:p:249-261
    DOI: 10.1016/j.jmva.2016.11.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X16301622
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.11.008?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. Alan Huang & Paul J. Rathouz, 2012. "Proportional likelihood ratio models for mean regression," Biometrika, Biometrika Trust, vol. 99(1), pages 223-229.
    2. Diao Guoqing & Ning Jing & qin jing, 2012. "Maximum Likelihood Estimation for Semiparametric Density Ratio Model," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-29, June.
    3. Alan Huang, 2014. "Joint Estimation of the Mean and Error Distribution in Generalized Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 186-196, March.
    4. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    5. Xiaodong Luo & Wei Yann Tsai, 2012. "A proportional likelihood ratio model," Biometrika, Biometrika Trust, vol. 99(1), pages 211-222.
    6. Michael S. Smith & Mohamad A. Khaled, 2012. "Estimation of Copula Models With Discrete Margins via Bayesian Data Augmentation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 290-303, March.
    7. Kung‐Yee Liang & Jing Qin, 2000. "Regression analysis under non‐standard situations: a pairwise pseudolikelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 773-786.
    8. D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564, September.
    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. Weibin Zhong & Guoqing Diao, 2023. "Joint semiparametric models for case‐cohort designs," Biometrics, The International Biometric Society, vol. 79(3), pages 1959-1971, September.
    2. Weibin Zhong & Guoqing Diao, 2023. "Semiparametric Density Ratio Model for Survival Data with a Cure Fraction," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 217-241, April.
    3. Zhang, Archer Gong & Chen, Jiahua, 2022. "Density ratio model with data-adaptive basis function," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    4. Marchese, Scott & Diao, Guoqing, 2018. "Joint regression analysis of mixed-type outcome data via efficient scores," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 156-170.

    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. Weibin Zhong & Guoqing Diao, 2023. "Joint semiparametric models for case‐cohort designs," Biometrics, The International Biometric Society, vol. 79(3), pages 1959-1971, September.
    2. Weibin Zhong & Guoqing Diao, 2023. "Semiparametric Density Ratio Model for Survival Data with a Cure Fraction," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 217-241, April.
    3. Marchese, Scott & Diao, Guoqing, 2018. "Joint regression analysis of mixed-type outcome data via efficient scores," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 156-170.
    4. Azam, Kazim & Pitt, Michael, 2014. "Bayesian Inference for a Semi-Parametric Copula-based Markov Chain," The Warwick Economics Research Paper Series (TWERPS) 1051, University of Warwick, Department of Economics.
    5. Azam, Kazim & Pitt, Michael, 2014. "Bayesian Inference for a Semi-Parametric Copula-based Markov Chain," Economic Research Papers 270232, University of Warwick - Department of Economics.
    6. Siem Jan Koopman & Rutger Lit & André Lucas & Anne Opschoor, 2018. "Dynamic discrete copula models for high‐frequency stock price changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 966-985, November.
    7. Qi Liu & Chun Li & Valentine Wanga & Bryan E. Shepherd, 2018. "Covariate†adjusted Spearman's rank correlation with probability†scale residuals," Biometrics, The International Biometric Society, vol. 74(2), pages 595-605, June.
    8. Pravin Trivedi & David Zimmer, 2017. "A Note on Identification of Bivariate Copulas for Discrete Count Data," Econometrics, MDPI, vol. 5(1), pages 1-11, February.
    9. Elizabeth D. Schifano & Himchan Jeong & Ved Deshpande & Dipak K. Dey, 2021. "Fully and empirical Bayes approaches to estimating copula-based models for bivariate mixed outcomes using Hamiltonian Monte Carlo," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 133-152, March.
    10. L. L. Henn, 2022. "Limitations and performance of three approaches to Bayesian inference for Gaussian copula regression models of discrete data," Computational Statistics, Springer, vol. 37(2), pages 909-946, April.
    11. Fokianos, Konstantinos, 2024. "Multivariate Count Time Series Modelling," Econometrics and Statistics, Elsevier, vol. 31(C), pages 100-116.
    12. Stöber, Jakob & Hong, Hyokyoung Grace & Czado, Claudia & Ghosh, Pulak, 2015. "Comorbidity of chronic diseases in the elderly: Patterns identified by a copula design for mixed responses," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 28-39.
    13. Ruben Loaiza-Maya & Michael Stanley Smith, 2017. "Variational Bayes Estimation of Discrete-Margined Copula Models with Application to Time Series," Papers 1712.09150, arXiv.org, revised Jul 2018.
    14. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    15. Hua Yun Chen & Daniel E. Rader & Mingyao Li, 2015. "Likelihood Inferences on Semiparametric Odds Ratio Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1125-1135, September.
    16. Bhaskar Bhattacharya & Mohammad Al-talib, 2017. "A minimum relative entropy based correlation model between the response and covariates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1095-1118, September.
    17. Zilko, Aurelius A. & Kurowicka, Dorota, 2016. "Copula in a multivariate mixed discrete–continuous model," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 28-55.
    18. Xiaotian Zheng & Athanasios Kottas & Bruno Sansó, 2023. "Bayesian geostatistical modeling for discrete‐valued processes," Environmetrics, John Wiley & Sons, Ltd., vol. 34(7), November.
    19. Diao Guoqing & Ning Jing & qin jing, 2012. "Maximum Likelihood Estimation for Semiparametric Density Ratio Model," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-29, June.
    20. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.

    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:jmvana:v:154:y:2017:i:c:p:249-261. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.