The Bayesian Group Lasso for Confounded Spatial Data

Trevor J. Hefley, Mevin B. Hooten, Ephraim M. Hanks, Robin E. Russell, Daniel P. Walsh

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

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. Supplementary materials accompanying this paper appear online.

Original languageEnglish (US)
Pages (from-to)42-59
Number of pages18
JournalJournal of Agricultural, Biological, and Environmental Statistics
Volume22
Issue number1
DOIs
StatePublished - Mar 1 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Agricultural and Biological Sciences (miscellaneous)
  • Environmental Science(all)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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