How we build geostatistical models and deal with their output

Pebesma E.J.

Forschungsartikel (Buchbeitrag)

Zusammenfassung

Multivariable linear geostatistical models extend multivariable, multiple linear regression models for cases where observations are spatially correlated, enabling the prediction of values at unobserved locations. In multiple linear regression, the goal is to explain a large part of the observed variability by a set of regressors and possibly their interactions. The more variability explained, the better the prediction. Geostatistics extends this by looking at spatial correlation in the residual variability: at a prediction location a nearby residual may carry predictive value to the residual value at that location. However, much of the geostatistical curriculum (literature and software) does not start off by attempting to explain variability in the observed variables, but rather starts at describing and modelling the observed variability after assuming the trend is a spatially constant, thereby potentially ignoring available informative predictors. Extensions are universal kriging and external drift kriging [5]. In universal kriging, only coordinates are used to explain variability. It is of no surprise that this has not become popular, as coordinates hardly ever carry a physical relation to the observed variable, and may lead to extreme, unrealistic extrapolations near the border of the domain. External drift kriging does extend kriging interpolation to the linear using a linear regression model with an external variable for the trend, but it is most often explained as being the case where only a single predictor (external drift variable) is present. In the following, we will not distinguish between universal kriging and external drift kriging, as the procedures are equivalent [7]. Multivariable prediction has been known for a long time, and has been applied especially when using one or more secondary variables to predict a primary variable. The general case where m variables are used to predict m variables, m being larger than say 3, is found seldom in literature. The reasons for this do not have a statistical ground, but rather stem from the fact that it is considered a burden to do so. Although algorithms exist to automate the modelling of many direct and cross variograms [10, 11, 24], easily accessible software implementations have been lacking. This paper discusses several limitations found in statistical software (mostly R) and Geographic Information Systems (GIS; [4]) software, with respect to flexible modelling of the multivariable linear geostatistical model. In a case study we show how to apply this model, using the recently developed gstat package for R and S-PLUS [20]. The discussion closes with a highly personalized view on the practice, limitations and possibilities of applied geostatistics. © 2009 Springer Berlin Heidelberg.

Details zur Publikation

Herausgeber*innen: Springer
Buchtitel: Interfacing Geostatistics and GIS
Seiten: 13
Veröffentlichungsjahr: 2009
Verlag: Springer Berlin Heidelberg
ISBN: 9783540332350
Sprache, in der die Publikation verfasst ist: Englisch
Link zum Volltext: http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84872154379