corRExpwr2Dt {ramps}R Documentation

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”, “temporal range”, and “space-time interaction” of the powered exponential correlation structure, all of which must be greater than zero. If nugget is TRUE, meaning that a nugget effect is present, value can contain four or five elements, the first four as described previously and the fifth the “nugget effect” (one minus the correlation between two observations taken arbitrarily close together); the first four must be greater than zero and the fifth must be between zero and one. Defaults to numeric(0), which results in a range of 90% of the minimum distance and a nugget effect of 0.1 being assigned to the parameters when object is initialized.
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 since the associated model includes a separate measurement error variance parameter.
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.
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.

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.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

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)

[Package ramps version 0.5-3 Index]