A0833
Title: Bayesian ridge estimators based on copula-based joint prior distributions for logistic regression parameters
Authors: Hirofumi Michimae - Kitasato University (Japan)
Yuto Aizawa - Kitasato university (Japan) [presenting]
Abstract: Ridge regression was originally proposed as an alternative to OLS regression in order to address multicollinearity in linear regression and later extended to logistic regression and also to Cox regression. In the Bayesian framework, the ridge estimator is interpreted as a Bayesian posterior mode when the regression coefficients have multivariate normal priors. We previously proposed vine copula-based joint priors on the regression coefficients in linear regression including an interaction, which promote the use of ridge regression because the interaction term produces multicollinearity. We showed that the vine copula-based priors improved the estimation accuracy over the multivariate normal prior, and would be a promising approach in other types of regression, such as logistic regression. We propose the vine copula-based prior for Bayesian ridge estimators under the logistic model. Especially, we focus on the case of two covariates and their interaction term. A simulation study was carried out to compare the performance of four prior (the Clayton, Gumbel, Gaussian priors and the trivariate normal prior) on the regression coefficients. These simulation studies proved that the Archimedean (the Clayton, Gumbel) copula priors showed more accurate estimates in the presence of multicollinearity compared with the other priors.
