POISSON COKRIGING AS A GENERALIZED LINEAR MIXED MODEL.

Area of Science:

• Environmental Science
• Ecology
• Biostatistics

Background:

• Spatially correlated count data, often following a Poisson distribution, are common in environmental and biological studies.
• Predicting these outcomes often requires incorporating auxiliary variables like temperature or precipitation.

Purpose of the Study:

• To introduce and evaluate Poisson cokriging, a Generalized Linear Mixed Model (GLMM), for predicting Poisson distributed count outcomes with auxiliary variables.
• To demonstrate the practical applicability and accuracy of this novel spatial prediction methodology.

Main Methods:

• Proposed a bivariate Generalized Linear Mixed Model (GLMM) incorporating Poisson outcome and auxiliary variables.
• Utilized a covariance structure analogous to traditional cokriging.
• Conducted a simulation study and applied the model to real-world fish microplastic count data.

Main Results:

• The Poisson cokriging methodology demonstrated successful application in practice.
• The model achieved small average prediction errors.
• Empirical coverage was close to the nominal 95% level, indicating reliable uncertainty estimation.

Conclusions:

• Poisson cokriging is a viable and effective tool for spatial prediction of count data.
• The model offers a robust approach for integrating auxiliary information in ecological and environmental health studies.
• The method provides accurate predictions with reliable uncertainty quantification.