Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models

• 成果类型: Article
• 署名作者: Scheipl, Fabian; Fahrmeir, Ludwig; Kneib, Thomas
• 署名单位: University of Munich; University of Gottingen
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.737742
• 发表日期: 2012
• 页码: 1518-1532
• 关键词: bayesian variable selection; variance; tests

摘要

Structured additive regression (STAR) provides a general framework for complex Gaussian and non-Gaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects, and further regression terms. The large flexibility, of STAR makes function selection a challenging and important task, aiming at (1) selecting the relevant covariates, (2) choosing an appropriate and parsimonious representation of the impact of covariates on the predictor, and (3) determining the required interactions. We propose a spike-and-slab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms. A novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a,Markov chain Monte Carlo simulation approach and is shown to induce desirable shrinkage properties. In-simulation studies-and with (real)-benchmark classification data; we investigate sensitivity to hyperparameter settings and compare performance to competitors. The flexibility and applicability of our approach are demonstrated in an additive piecewise exponential model with time-varying effects for right-censored survival times of intensive care patients with sepsis. Geoadditive and additive mixed logit model applications are discussed in an extensive online supplement.