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Member Research & Reports

Member Research & Reports

UNMC: Poisson Cokriging as a Generalized Linear Mixed Model

It is often of interest to predict spatially correlated count outcomes that follow a Poisson distribution. For example, in the environmental sciences we may want to predict pollen counts using temperature or precipitation data as auxiliary variables. Kriging has been the traditional method for prediction of spatially correlated normally distributed data and has been employed for prediction of count data. Dr. Lynette Smith from the University of Nebraska Medical Center College of Public Health, has proposed Poisson cokringing as a Generalized Linear Mixed Model (GLMM) to predict a Poisson outcome variable in the presence of an auxiliary variable. Dr. Smith and colleagues have published the results of their work titled “Poisson cokriging as a generalized linear mixed model” in the current issue of Spatial Statistics.

Dr. Smith and colleagues proposed model has a bivariate structure with a Poisson outcome variable and an auxiliary variable. A covariance matrix similar to that used in cokriging is assumed. The authors present a  simulation study and a real data example using the number of microplastics in the digestive tracts of fish. They show that Poisson cokriging methodology can be applied successfully in practice with small average errors and coverage close to 95 percent. The Poisson cokriging model can be a useful tool for spatial prediction. This method can fill a need in spatial prediction allowing flexibility in the choice of distributions for the variables of interest and allowing prediction when the auxiliary variable is not collocated with the primary outcome variable.

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