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Density ratio model for multivariate outcomes

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  • 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
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    References listed on IDEAS

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    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.
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    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.
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    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.

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