corRGneit function

Gneiting Spatial Correlation Structure

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 $d >= r / s$ the correlation is zero.

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.

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.

Returns

Object of class 'corRGneit', also inheriting from class 'corRSpatial', 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.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

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)