ramps (version 0.6-12)

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, and $s$ the scale, the correlation between two observations a distance $d$ apart is $1/(2^{s-1} \Gamma(s)) (d/r)^s K_s(d/r)$.

Usage

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

Arguments

value

optional numeric vector of two parameter values for the Matern correlation structure, corresponding to the range and scale. The range parameter value must be greater than zero, and the scale in the interval (0, 2]. Defa

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 '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)