ramps (version 0.6-12)

corRExpwr2: Non-Separable Powered Exponential Spatio-Temporal Correlation Structure

Description

This function is a constructor for the 'corRExpwr2' class, representing a non-separable spatial correlation structure. Letting $rs$ denote the spatial range, $ps$ the spatial shape, $rt$ the temporal range, $pt$ the temporal shape, and $lambda$ the space-time interaction, the correlation between two observations a distance $d$ apart in space and $t$ in time is $\exp(-(d/rs)^ps - (t/rt)^pt - \lambda (d/rs)^ps (t/rt)^pt)$.

Usage

corRExpwr2(value = numeric(0), form = ~ 1,
              metric = c("euclidean", "maximum", "manhattan", "haversine"),
              radius = 3956)

Arguments

value

optional numeric vector of five parameter values for the powered exponential correlation structure, corresponding to the spatial range, spatial shape, temporal range, temporal shape, and

form

one-sided formula of the form ~ S1+...+Sp+T, specifying spatial covariates S1 through Sp and the times T at which measurement were taken.

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 'corRExpwr2', inheriting from class 'corSpatioTemporal', representing a non-separable spatial correlation structure.

References

Cressie, N. and Huang, H.-C. (1993) Classes of Nonseperable, Spatio-Temporal Stationary Covariance Functions, Journal of the American Statistical Association, 94, 1330-1340. Gneiting, T. (2002) Nonseparable, stationary covariance functions for space-time data, Journal of the American Statistical Association, 97, 590-600.

See Also

corClasses, Initialize.corStruct, summary.corStruct

Examples

sp1 <- corRExpwr2(form = ~ x + y + t)

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

cs1Expwr <- corRExpwr2(c(1, 1, 1, 1, 1), form = ~ x + y + t)
cs1Expwr <- Initialize(cs1Expwr, spatDat)
corMatrix(cs1Expwr)

cs2Expwr <- corRExpwr2(c(1, 1, 1, 1, 1), form = ~ x + y + t, metric = "man")
cs2Expwr <- Initialize(cs2Expwr, spatDat)
corMatrix(cs2Expwr)