ramps (version 0.6.18)

corRCauchy: Cauchy Spatial Correlation Structure

Description

This function is a constructor for the 'corRCauchy' class, representing a Cauchy (rational quadratic) spatial correlation structure. Letting \(r\) denote the range, the correlation between two observations a distance \(d\) apart is \(1/(1+(d/r)^2)\).

Usage

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

Value

Object of class 'corRCauchy', also inheriting from class 'corRSpatial', representing a rational quadratic spatial correlation structure.

Arguments

value

optional numeric “range” parameter value for the rational quadratic 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 (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.

Author

Brian Smith and Jose Pinheiro , and Douglas Bates

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

corRClasses

Examples

sp1 <- corRCauchy(form = ~ x + y + z)

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

cs1Cauchy <- corRCauchy(1, form = ~ x + y)
cs1Cauchy <- Initialize(cs1Cauchy, spatDat)
corMatrix(cs1Cauchy)

cs2Cauchy <- corRCauchy(1, form = ~ x + y, metric = "man")
cs2Cauchy <- Initialize(cs2Cauchy, spatDat)
corMatrix(cs2Cauchy)