Modeling Spatial Patterns In Bycatch Analyses Using The Delta Model Modified With Eigenfunction-Based Spatial Filters

Incorporation of spatial dependence in bycatch modeling has been challenging because the bycatch data usually contain high percentage of zero observations and involve large dataset that may require intensive computing.  The eigenfunction-based spatial filtering provides a flexible tool that allows the existing bycatch modeling approaches such as the delta model to be applied in the presence of spatial dependence. The present study demonstrated an application of the delta model modified with the spatial filters in bycatch analysis using a real dataset, the seabird bycatch data from the National Marine Fisheries Service Pelagic Observer Program during 1992-2011. We explored a total of 108 spatial weighting matrices and found that the best matrix was constructed with the Gabriel graph connectivity matrix and the exponential weighting function with parameter m = 0.5. We modified the delta model by incorporating the spatial filters generated from the best spatial weighting matrix. We applied the five-fold cross-validation to compare performance of the modified delta model with other three candidate models based on the mean absolute error and the mean bias. Results confirmed that the delta model modified with spatial filters showed superiority over the other three candidate models in seabird bycatch assessment.