corRGneit {ramps}

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 when object is initialized.

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 the sum of the absolute differences; and "haversine" for the great-circle distance between longitude/latitude coordinates. Partial matching of arguments is used, so only the first three characters need to be provided. Defaults to "euclidean".

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 'corRSpatial', representing the Gneiting spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith [e-mail]

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

corRClasses

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)