Spatial Prediction of Poisson Response Variable with Covariate

• Activity Number: 344
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Lynette M. Smith*+ and David B. Marx
• Companies: University of Nebraska Medical Center and University of Nebraska
• Keywords: spatial prediction ; Poisson ; NORTA

Abstract

It is often of interest to predict spatially correlated count data such as that arising from disease incidence or mortality rates. A generalized linear mixed model (GLMM) approach to prediction using Poisson response variable conditional on the spatial location is simulated using G-side models. We simulated data from a Poisson distribution with a spherical correlation structure and separately co-simulated covariates correlated with the original variable from Gaussian, Binomial and Beta distributions. This was accomplished using NORTA (Normal to Anything) after simulating a bivariate spatial Gaussian structure. We compared prediction of unobserved spatial locations under various conditions: entire response variable (Poisson) available or fractions of it missing and the entire covariate (Gaussian, Binomial or Beta) or some of it missing. We also fit a multivariate GLMM with both the Poisson variable and the covariate as outcome variables to compare its prediction with the other scenarios as described. The addition of a covariate improved prediction in the GLMM models, as expected. However, the comparison of interest is looking at the effect of the various covariate distributions.