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. To predict a Poisson outcome variable in the presence of an auxiliary variable, Poisson cokriging as a Generalized Linear Mixed Model (GLMM) is proposed. This 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. A simulation study and a real data example using the number of microplastics in the digestive tracts of fish are presented. The results showed that Poisson cokriging methodology can be applied successfully in practice with small average errors and coverage close to 95%. The Poisson cokriging model can be a useful tool for spatial prediction.