ramps (version 0.6-12)

corRGneit: Gneiting Spatial Correlation Structure

Description

This function is a constructor for the 'corRGneit' class, representing the Gneiting approximation to the Gaussian correlation structure. Letting $r$ denote the range, the correlation between two observations a distance $d < r / s$ apart is $(1 + 8 s x + 25 (s x)^2 + 32 (s x)^3) (1 - s x)^8$, where s = 0.301187465825. If $d \geq r / s$ the correlation is zero.

Usage

corRGneit(value = numeric(0), form = ~ 1,
             metric = c("euclidean", "maximum", "manhattan", "haversine"),
             radius = 3956)

Arguments

value

optional numeric range parameter value for the Gneiting correlation structure, which must be greater than zero. Defaults to numeric(0), which results in a range of 90% of the minimum distance being assigned to the parameter

form

one-sided formula of the form ~ S1+...+Sp, specifying spatial covariates S1 through Sp. Defaults to ~ 1, which corresponds to using the order of the observations in the data as a covariate.

metric

optional character string specifying the distance metric to be used. The currently available options are "euclidean" for the root sum-of-squares of distances; "maximum" for the maximum difference; "manhattan" for t

radius

radius to be used in the haversine formula for great-circle distance. Defaults to the Earth's radius of 3,956 miles.

Value

• Object of class 'corRGneit', also inheriting from class 'corSpatial', representing the Gneiting spatial correlation structure.

References

Gneiting, T. (1999), Correlation Functions for Atmospheric Data Analysis, Quarterly Journal of the Royal Meteorological Society, 125(559), 2449-2464.

Venables, W.N. and Ripley, B.D. (1997) Modern Applied Statistics with S-plus, 2nd Edition, Springer-Verlag.

See Also

corClasses, Initialize.corStruct, summary.corStruct

Examples

sp1 <- corRGneit(form = ~ x + y + z)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4)

cs1Gneit <- corRGneit(1, form = ~ x + y)
cs1Gneit <- Initialize(cs1Gneit, spatDat)
corMatrix(cs1Gneit)

cs2Gneit <- corRGneit(1, form = ~ x + y, metric = "man")
cs2Gneit <- Initialize(cs2Gneit, spatDat)
corMatrix(cs2Gneit)