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Bayesian Model Selections for Log-binomial Regression

Zhou, Wei
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1544101297752931

Abstract Details

2018, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
In epidemiology and clinical research, the relative risk (RR) is commonly used as a measure of the risk of developing a disease. The log-binomial regression is a preferred statistical model to estimate RR as it provides a convenient form of RR. However, the constrained parameter space of the log-binomial model often causes numerical difficulties in applying this model for data analysis. In this dissertation, we conduct model selections for the log-binomial regression where three objectives are addressed. Firstly, we develop Bayesian variable selection methods for log-binomial model, where the Bayes factor is used as the selection criterion and five Monte Carlo methods are utilized to compute the Bayes factor while dealing with the constrained parameter space. These Monte Carlo methods are then assessed for computational accuracy and efficiency. Secondly, we study the sensitivity of Bayes factor to the prior distributions of the regression parameters by evaluating the performances of five popular priors in the log-binomial variable selection, i.e. independent Gaussian prior, independent t prior, independent Cauchy prior, the g-prior (g=n) and the Zellner-Siow Cauchy prior. Finally, we perform Bayesian model selection between the log-binomial and the logistic regressions where the Bayes factor, the fractional Bayes factor, LPML, DIC and BIC are used as the model selection methods. In addition, four prior densities of the regression parameters are considered: the flat prior, Cauchy prior, Jeffreys prior and an elicited proper prior. The theoretical properties of these priors are also investigated. These methods and priors are compared via simulations on their capabilities of distinguishing between the log-binomial and logit models.
Siva Sivaganesan, Ph.D. (Committee Chair)
Emily Kang, Ph.D. (Committee Member)
Seongho Song, Ph.D. (Committee Member)
Xia Wang, Ph.D. (Committee Member)
129 p.
Statistics
Log-binomial Regression; Bayesian Model Selection; Bayesian Variable Selection; Monte Carlo methods; Bayes factor; Relative Risk

Recommended Citations

Citations

  • Zhou, W. (2018). Bayesian Model Selections for Log-binomial Regression [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1544101297752931

    APA Style (7th edition)

  • Zhou, Wei. Bayesian Model Selections for Log-binomial Regression. 2018. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1544101297752931.

    MLA Style (8th edition)

  • Zhou, Wei. "Bayesian Model Selections for Log-binomial Regression." Doctoral dissertation, University of Cincinnati, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1544101297752931

    Chicago Manual of Style (17th edition)

ucin1544101297752931
189
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This open access ETD is published by University of Cincinnati and OhioLINK.