ramps (version 0.5-2)

corRMatern: Matern Spatial Correlation Structure

Description

This function is a constructor for the 'corRMatern' class, representing a Matern spatial correlation structure. Letting $r$ denote the range, $s$ the shape, and $n$ the nugget effect, the correlation between two observations a distance $d$ apart is $1/(2^{s-1} \Gamma(s)) (d/r)^s K_s(d/r)$ when no nugget effect is present and $(1-n) 1/(2^{s-1} \Gamma(s)) (d/r)^s K_s(d/r)$ when a nugget effect is assumed.

Usage

corRMatern(value = numeric(0), form = ~ 1, nugget = FALSE,
              metric = c("euclidean", "maximum", "manhattan", "haversine"),
              radius = 3956, fixed = FALSE)

Arguments

value

optional vector with the parameter values in constrained form. If nugget is FALSE, value can have only two elements, corresponding to the range and scale of the Matern correlation st

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, and no groups

nugget

optional logical value indicating whether a nugget effect is present. Defaults to FALSE. This argument exists for consistency with the nlme library and should be left set at its default value when used in georamps s

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.

fixed

optional logical value indicating whether the coefficients should be allowed to vary or be kept fixed at their initial value. This argument exists for consistency with the nlme library and is ignored in the ramps algorithm.

Value

• Object of class 'corRMatern', also inheriting from class 'corSpatial', representing a Matern spatial correlation structure.

References

Cressie, N.A.C. (1993), Statistics for Spatial Data, J. Wiley & Sons. 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 <- corRMatern(form = ~ x + y + z)

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

cs1Matern <- corRMatern(c(1, 1), form = ~ x + y)
cs1Matern <- Initialize(cs1Matern, spatDat)
corMatrix(cs1Matern)

cs2Matern <- corRMatern(c(1, 1), form = ~ x + y, metric = "man")
cs2Matern <- Initialize(cs2Matern, spatDat)
corMatrix(cs2Matern)

cs3Matern <- corRMatern(c(1, 1, 0.2), form = ~ x + y, nugget = TRUE)
cs3Matern <- Initialize(cs3Matern, spatDat)
corMatrix(cs3Matern)