HANDOUT 7: Model Selection
This handout illustrates some methods for model selection:
AIC, BIC and cross validation.
Cross Validation.
Consider again the spatial rainfall data set “darwinw.dat”.
We entertain four models for this data set. The models have all a constant mean function
and no nugget, but they differ in the semivariogram function:
Model 1: Power exponential model with θ2= 1 (kappa in geoR) ;
Model 2: Power exponential model with θ2= 1.5 ;
Model 3: Mat´ern model with θ2= 1 ;
Model 4: Rational quadratic with θ2= 2 ;
> library(geoR)
##
## A possible criterion to select model is based how well each
## semivariogram model fits the empirical semivariogram, measured by the
## weighted residual sum of squares evaluated at the estimated values
##
> darwin.wls1 <- variofit(darwin.mom9, cov.model = "exp", ini = c(800,10),
+ fix.nugget = T, nugget = 0, weights = "cressie") ## Model 1
> darwin.wls4 <- variofit(darwin.mom9, cov.model = "powered.exp", ini = c(800,10),
+ fix.nugget = T, nugget = 0, weights = "cressie", kappa = 1.5) ## Model 2
> darwin.wls5 <- variofit(darwin.mom9, cov.model = "matern", ini = c(100,5),
+ fix.nugget = T, nugget = 0, weights = "cressie", kappa = 1) ## Model 3
> darwin.wls6 <- variofit(darwin.mom9, cov.model = "cauchy", ini = c(100,1),
+ fix.nugget = T, nugget = 0, weights = "cressie", kappa = 2) ## Model 4
>
> darwin.wls1$value ; darwin.wls4$value ; darwin.wls5$value ; darwin.wls6$value
[1] 7.485468
[1] 4.564043
[1] 4.658527
[1] 3.461156
##
## According to this criterion, Model 4 provides the best fit
##
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