ramps (version 0.5-2)

corRExpwr2Dt: Non-Separable Temporally Integrated Powered Exponential Spatial Correlation Structure

Description

This function is a constructor for the 'corRExpwr2Dt' class, representing a non-separable spatial correlation structure for temporally integrated measurements. Letting $rs$ denote the spatial range, $ps$ the spatial shape, $rt$ the temporal range, $lambda$ the space-time interaction, and $n$ the nugget effect, the correlation between two observations a distance $d$ apart in space and $t$ in time is $\exp(-(d/rs)^ps - t/rt - \lambda (d/rs)^ps (t/rt))$ when no nugget effect is present and $(1-n) \exp(-(d/rs)^ps - t/rt - \lambda (d/rs)^ps (t/rt))$ when a nugget effect is assumed.

Usage

corRExpwr2Dt(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 four elements, corresponding to the spatial range, spatial shape, tempo

form

one sided formula of the form ~ S1+...+Sp+T1+T2, specifying spatial covariates S1 through Sp and the times (T1, T2) at which measurement periods begin and end, respectively.

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 'corRExpwr2Dt', also inheriting from class 'corSpatial', 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. Smith, B.J. and Oleson, J.J. (2007) Geostatistical Hierarchical Model for Temporally Integrated Radon Measurements, Jounal of Agricultural, Biological, and Environmental Statistics, in press.

See Also

corClasses, Initialize.corStruct, summary.corStruct

Examples

sp1 <- corRExpwr2Dt(form = ~ x + y + t1 + t2)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4, t1=(0:4)/4, t2=(1:5)/4)

cs1ExpwrDt <- corRExpwr2Dt(c(1, 1, 1, 1), form = ~ x + y + t1 + t2)
cs1ExpwrDt <- Initialize(cs1ExpwrDt, spatDat)
corMatrix(cs1ExpwrDt)

cs2ExpwrDt <- corRExpwr2Dt(c(1, 1, 1, 1), form = ~ x + y + t1 + t2, metric = "man")
cs2ExpwrDt <- Initialize(cs2ExpwrDt, spatDat)
corMatrix(cs2ExpwrDt)

cs3ExpwrDt <- corRExpwr2Dt(c(1, 1, 1, 1, 0.2), form = ~ x + y + t1 + t2, nugget = TRUE)
cs3ExpwrDt <- Initialize(cs3ExpwrDt, spatDat)
corMatrix(cs3ExpwrDt)