GRASP: generalized regression analysis and spatial prediction

Abstract

We present generalized regression analysis and spatial prediction (GRASP) conceptually as a method for producing spatial predictions using statistical models, and introduce and demonstrate a specific implementation in Splus that facilitates the process. We put forward GRASP as a new name encapsulating an existing concept that aims at making spatial predictions using generalized regression analysis. Regression modeling is used to establish relationships between a response variable and a set of spatial predictors. The regression relationships are then used to make spatial predictions of the response. The GRASP process requires point measurements of the response, as well as regional coverages of predictor variables that are statistically (and preferably causally) important in determining the patterns of the response. This approach to spatial prediction is becoming more commonplace, and it is useful to define it as a general concept. For instance, GRASP could use a survey of the abundance of a species (the response), and existing spatial coverages of environmental (e.g. climate, landform) variables (the predictors) for a region. A multiple regression can be used to establish the statistical relationship between the species abundance and the environmental variables. These regression relationships can then be used to predict the species abundance from the environmental surfaces. This process defines relationships in environmental space and uses these relationships to predict in geographic space. We introduce GRASP (the implementation) as an interface and collection of functions in Splus designed to facilitate modern regression analysis and the use of these regressions for making spatial predictions. GRASP standardizes the modeling process and makes it more reproducible and less subjective, while preserving analysis flexibility. The set of functions provides a toolbox that allows quick and easy data checking, model building and evaluation, and calculation of predictions. The current version uses generalized additive models (GAMs), a modern non-parametric regression technique the advantages of which are discussed. We demonstrate the use of the GRASP implementation to model and predict the natural distributions of two components of New Zealand fern biodiversity: (1) the natural distribution of an icon species, silver fern (Cyathea dealbata); and (2) the natural pattern of total fern species richness. Key steps are demonstrated, including data preparation, options setting, data exploration, model building, model validation and interpretation, and spatial prediction.