A Model-based Analysis of Semicontinuous Spatial Data
Open Access
- Author:
- Recta, Virginia F.
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- January 28, 2009
- Committee Members:
- James Landis Rosenberger, Dissertation Advisor/Co-Advisor
James Landis Rosenberger, Committee Chair/Co-Chair
Murali Haran, Committee Chair/Co-Chair
Joseph Francis Schafer, Committee Member
Shelby Jay Fleischer, Committee Member - Keywords:
- model-based geostatistics
zero-inflated data
spatial GLMM
semicontinuous data
two-stage model - Abstract:
- We consider the problem of modeling point-level (‘geostatistical’) spatial count data with a large number of zeros. We develop a model that is compatible with the scientific assumptions about the data generating process. We use a two-stage spatial generalized linear mixed model framework for the counts, modeling incidence, resulting in 0-1 outcomes, and abundance, resulting in positive counts, as separate but dependent processes, and utilize a bivariate Gaussian process model for characterizing the underlying spatial dependence. We describe a Bayesian approach and study several variants of our two-stage model, consisting of varying covariance and cross-covariance structures for the underlying bivariate Gaussian random process. We fit the models via Markov chain Monte Carlo (MCMC) methods We study several MCMC algorithms, including a version of the Langevin-Hastings algorithm, for exploring the complicated posterior distribution efficiently, and recommend an algorithm that is fairly automated. Finally, we demonstrate the application of our modeling and computational approach on both simulated data and a real data set from an ecological study and compare the performance of the various two-stage models based on inference and prediction.