corRExpwr2Dt function

Non-Separable Temporally Integrated Powered Exponential Spatial Correlation Structure

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 $exp(-(d/rs)^ps - t/rt - lambda * (d/rs)^ps * (t/rt))$.

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 . The range parameter values must be greater than zero, the shape in the interval (0, 2], and the interaction greater than or equal to zero. Defaults to numeric(0), which results in ranges of 90% of the minimum distances, a shape of 1, and an interaction of 0 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.
• 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.

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.

Returns

Object of class 'corRExpwr2Dt', also inheriting from class 'corRSpatial', representing a non-separable spatial correlation structure.

References

Cressie, N. and Huang, H.-C. (1993) Classes of Nonseperable, Spatio-Temporal Stationary CovarianceFunctions , Journal of the American Statistical Association, 94, 1330-1340.

Smith, B.J. and Oleson, J.J. (2007) Geostatistical Hierarchical Model for Temporally Integrated RadonMeasurements , Jounal of Agricultural, Biological, and Environmental Statistics, in press.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

See Also

corRClasses

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)