Modeling spatial patterns of rare species using eigenfunction-based spatial filters: An example of modified delta model for zero-inflated data

Data of rare species usually contain a high percentage of zero observations due to their low abundance. Such data are generally referred as zero-inflated data. Modeling spatial patterns in such data has been challenging, especially when large datasets are involved and intensive computing are required. The eigenfunction-based spatial filtering provides a flexible tool that allows the existing modeling approaches that can handle zero-inflated data such as the delta model to be applied in the presence of spatial dependence. With a real dataset, the longline seabird bycatch data, the present study demonstrated a modification of delta model with the spatial filters to investigate spatial patterns in zero-inflated data for rare species. We explored a total of 108 spatial weighting matrices, and 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. The three candidate models included the baseline model without spatial dependence considered, the trend-surface generalized additive model and the random areal effect model. The delta model modified with spatial filters showed superior performance over the other three candidate models in the seabird bycatch example. With the seabird bycatch example, we illustrated a modification of delta model with the eigenfunction-based spatial filters to investigate spatial patterns. This study provides an alternative to incorporate spatial dependence in the existing approaches for modeling spatial patterns in zero-inflated data for rare species.