# corRExpwr: Powered Exponential Spatial Correlation Structure In brian-j-smith/ramps: Bayesian Geostatistical Modeling with RAMPS

## Description

This function is a constructor for the `'corRExpwr'` class, representing a powered exponential spatial correlation structure. Letting r denote the range and p the shape, the correlation between two observations a distance d apart is exp(-(d/r)^p).

## Usage

 ```1 2 3``` ``` corRExpwr(value = numeric(0), form = ~ 1, metric = c("euclidean", "maximum", "manhattan", "haversine"), radius = 3956) ```

## Arguments

 `value` optional numeric vector of two parameter values for the powered exponential correlation structure, corresponding to the “range” and “shape”. The range parameter value must be greater than zero, and the shape in the interval (0, 2]. Defaults to `numeric(0)`, which results in a range of 90% of the minimum distance and a shape of 1 being assigned to the parameter when `object` is initialized. `form` one-sided formula of the form `~ S1+...+Sp`, specifying spatial covariates `S1` through `Sp`. Defaults to `~ 1`, which corresponds to using the order of the observations in the data as a covariate. `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.

## Value

Object of class `'corRExpwr'`, also inheriting from class `'corRSpatial'`, representing a powered exponential 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 [email protected]

## References

Cressie, N.A.C. (1993), “Statistics for Spatial Data”, J. Wiley & Sons.

Venables, W.N. and Ripley, B.D. (1997) “Modern Applied Statistics with S-plus”, 2nd Edition, Springer-Verlag.

`corRClasses`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```sp1 <- corRExpwr(form = ~ x + y + z) spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4) cs1Expwr <- corRExpwr(c(1, 1), form = ~ x + y) cs1Expwr <- Initialize(cs1Expwr, spatDat) corMatrix(cs1Expwr) cs2Expwr <- corRExpwr(c(1, 1), form = ~ x + y, metric = "man") cs2Expwr <- Initialize(cs2Expwr, spatDat) corMatrix(cs2Expwr) ```