B0686
Title: Statistical inference with anchored Bayesian mixture of regressions models
Authors: Deborah Kunkel - Clemson University (United States) [presenting]
Mario Peruggia - The Ohio State University (United States)
Abstract: An illustrative study is presented in which a mixture of regression models is used to improve an ill-fitting simple linear regression model relating log brain mass to log body mass for 100 placental mammalian species. A finite mixture of regression models may address lack-of-fit in a simple regression model by accounting for latent factors that produce heterogeneity in the response. An anchored Bayesian mixture of regressions model is presented, which modifies the standard Bayesian Gaussian mixture by pre-assigning small subsets of observations to given mixture components with probability one. These observations (called anchor points) break the relabeling invariance (or label-switching) typical of exchangeable models. A strategy for selecting anchor points is developed using tools from case influence diagnostics. The estimated covariances among log case-deletion weights are used to identify sub-groups of observations that have a similar influence on the regression analysis. Representative points of these clusters are selected to be anchor points in subsequent modelling. An anchoring strategy is also presented based on the expectation-maximization algorithm, and the anchoring methods are compared in mixture-of-regressions settings.
