ramps (version 0.6-12)

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, and $lambda$ the space-time interaction, the correlation between two observations a distance $d$ apart in space and $t$ in time is $\exp(-(d/rs)^ps - t/rt - \lambda (d/rs)^ps (t/rt))$.

Usage

corRExpwr2Dt(value = numeric(0), form = ~ 1,
                metric = c("euclidean", "maximum", "manhattan", "haversine"),
                radius = 3956)

Arguments

value

optional numeric vector of four parameter values for the powered exponential correlation structure, corresponding to the spatial range, spatial shape, temporal range, and space-time interaction

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.

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 '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)