Locally Accurate Prediction Standard Errors with Spatially Varying Regression coefficient Models

Paul Harris1, Stewart Fotheringham1 and Chris Brunsdon2

1. National Centre for Geocomputation University of Ireland Maynooth Maynooth, Co. Kildare, Ireland
2. Department of Geography University of Leicester Leicester, LEI 7RH, UK
1. {paul.harris, stewart.fotheringham}@num.ie
2. cbl79@le.ac.uk

Abstract: This study assesses the prediction and prediction uncertainty performance of models that cater for both: (i) a nonstationary relationship between the response and a contextual variable and (ii) a nonstationary residual variance (or variogram), at point locations for a single realisation spatial process. Here the crucial aspect of the model specification is allowing the residual variance (or variogram) to vary across space. Without this, the estimated prediction standard errors are only likely to be accurate in a global (or overall) sense and not the desired, local sense. Locally-accurate prediction standard errors, allow locally-relevant prediction confidence intervals and/or locally-relevant estimates of risk (e.g. the risk of exceeding some critical threshold) which is not only valuable to researchers who attempt to model spatial processes, but also to policy makers who need to plan and manage the outcomes of spatial processes at different spatial scales.

Keywords: georaphically weighted regression, moving window kriging, heteroskedastic, bayesian prediction models

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