The Bayesian Group Lasso for Confounded Spatial Data

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• 作者：Trevor J. Hefley ; Mevin B. Hooten…
• 关键词：Collinearity ; Dimension reduction ; Generalized linear mixed model ; Spatial confounding
• 刊名：Journal of Agricultural, Biological and Environmental Statistics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：22
• 期：1
• 页码：42-59
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics for Life Sciences, Medicine, Health Sciences; Agriculture; Monitoring/Environmental Analysis; Biostatistics;
• 出版者：Springer US
• ISSN：1537-2693
• 卷排序：22

文摘

Generalized linear mixed models for spatial processes are widely used in applied statistics. In many applications of the spatial generalized linear mixed model (SGLMM), the goal is to obtain inference about regression coefficients while achieving optimal predictive ability. When implementing the SGLMM, multicollinearity among covariates and the spatial random effects can make computation challenging and influence inference. We present a Bayesian group lasso prior with a single tuning parameter that can be chosen to optimize predictive ability of the SGLMM and jointly regularize the regression coefficients and spatial random effect. We implement the group lasso SGLMM using efficient Markov chain Monte Carlo (MCMC) algorithms and demonstrate how multicollinearity among covariates and the spatial random effect can be monitored as a derived quantity. To test our method, we compared several parameterizations of the SGLMM using simulated data and two examples from plant ecology and disease ecology. In all examples, problematic levels multicollinearity occurred and influenced sampling efficiency and inference. We found that the group lasso prior resulted in roughly twice the effective sample size for MCMC samples of regression coefficients and can have higher and less variable predictive accuracy based on out-of-sample data when compared to the standard SGLMM.