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Spatially Assessing Model Error Using Geographically Weighted Regression

LAFFAN, S.W. (Shawn.Laffan@anu.edu.au), Australian National University, Department of Geography, Canberra, 0200, Australia

Key Words: geographically weighted regression, error assessment, neural network, expert system

This research develops a method to identify local areas where a model has performed well when predicting some spatial distribution.

There is increasing interest in the use of non-spatial tools such as expert systems and artificial neural networks for mapping continuous or fuzzy spatial properties. This is because they can deal with more ancillary variables than spatial interpolation techniques such as co-kriging. Non-spatial tools do not provide truly spatial error measures so it is important to assess their spatial performance in order to identify local areas of acceptable prediction. These areas may then be used with confidence. Areas where there is not acceptable prediction may indicate the need for other variables in the model, or a different approach.

The method uses a variant of Geographically Weighted Regression (GWR) (Brunsdon et al., 1996). Measured values are compared with predicted values within circles of increasing size to allow the visualisation of error at increasing scales. No spatial weighting scheme is used. GWR is used because it allows the calculation of error values without transforming the original values to error residuals, and over locations where there is no measured data. The error is the square root of the area between the optimal 1:1 line and a fitted line, bounded by the maximum and minimum predicted values. The R-squared value indicates confidence in the assessment and is used to determine the best spatial scale.

The method is demonstrated using results from an artificial neural network trained to infer aluminum oxide percentages across a 1,100-square-km area in Weipa, far north Queensland, Australia.


Brunsdon, C., A.S. Fotheringham, and M.E. Charlton, 1996; Geographically Weighted Regression - A Method for Exploring Spatial Nonstationarity, Geographical Analysis, 28 (4), 281-298.