corRMatern function

Matern Spatial Correlation Structure

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 $1/(2^(s-1)*gamma(s))*(d/r)^s*besselK(d/r, s)$.

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]. Defaults to numeric(0), which results in a range of 90% of the minimum distance and a scale of 0.5 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 (miles) 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 'corRMatern', also inheriting from class 'corRSpatial', 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.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

See Also

corRClasses

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)