# corRCauchy: Cauchy Spatial Correlation Structure In brian-j-smith/ramps: Bayesian Geostatistical Modeling with RAMPS

## Description

This function is a constructor for the `'corRCauchy'` class, representing a Cauchy (rational quadratic) spatial correlation structure. Letting r denote the range, the correlation between two observations a distance d apart is 1/(1+(d/r)^2).

## Usage

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

## Arguments

 `value` optional numeric “range” parameter value for the rational quadratic correlation structure, which must be greater than zero. Defaults to `numeric(0)`, which results in a range of 90% of the minimum distance 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 `'corRCauchy'`, also inheriting from class `'corRSpatial'`, representing a rational quadratic 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] and Jose Pinheiro [email protected], and Douglas Bates [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 <- corRCauchy(form = ~ x + y + z) spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4) cs1Cauchy <- corRCauchy(1, form = ~ x + y) cs1Cauchy <- Initialize(cs1Cauchy, spatDat) corMatrix(cs1Cauchy) cs2Cauchy <- corRCauchy(1, form = ~ x + y, metric = "man") cs2Cauchy <- Initialize(cs2Cauchy, spatDat) corMatrix(cs2Cauchy) ```