A Computational Bayesian Method for Generalized Semiparametric Regression Models

Abstract

To better understand the power shift and the U.S. role compared to China and others regional actors, the Chicago Council on Global Affairs and the East Asia Institute (EAI) surveyed people in six countries - China, Japan, South Korea, Vietnam, Indonesian, and the United States - in the first half of 2008 about regional security and economic integration in Asia and about how these nations perceive each other (Bouton et al., 2010). There exists latent variance that cannot be adequately explained by parametric models. This is, in large part, due to the hidden structures and latent stories that from in unexpected ways. Therefore, a new Gibbs sampler is developed here in order to reveal preciously unseen structures and latent variances found in the survey dataset of Bouton et al. This new sampler is based upon the semiparametric regression, a well-known tool frequently utilized in order to capture the functional dependence between variables with fixed effect parametric and nonlinear regression. This is then extended to a generalized semiparametric regression for binary responses with logit and probit link function. The new sampler is then developed for the generalized linear mixed model with a nonparametric random effect. It is expressed as nonparametric regression with the multinomial-Dirichlet distribution for the number and positions of knots.