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Spatial Smoothing - Cont
Despite the complexity of the description of spatial smoothing, it can be implemented very efficiently in the S-Plus programming language. In the following programming statement, lo represents the loess function, while latitude and longitude are the projected coordinates of the county midpoints. The span of 1 defines each neighborhood as consisting of the nearest 100% of points in the sample space. Also, the dependent variable uses the untransformed loss costs, with the transformation being performed by the logit function.
- gam(loss.cost ~ lo(longitude, latitude, span = 1),
- family = quasi (link = logit, variance = "constant"),
- data = your.data, weights = liability, na.action = na.omit)
From a practical standpoint, the primary weakness of spatial smoothing is its complexity, which increases the difficulty of explaining the results to insurance regulators. Since the analysis cannot be reproduced in a spreadsheet, the reliability of the results cannot be easily confirmed.
The loess procedure is actually a simple form of spatial smoothing. More sophisticated forms of spatial smoothing have been developed, but these require a knowledge of the field of spatial statistics.
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