ncf (version 1.1-2)

spline.correlog: Uni- and multivariate spline correlograms

Description

spline.correlog is the function to estimate the spline (cross-)correlogram from spatial data. Either univariate or multivariate (time seres) for each site can be used.

Usage

spline.correlog(x, y, z, w = NULL, df = NULL, type = "boot", 
resamp = 1000, npoints = 300, save = FALSE, filter = FALSE, 
fw = 0, max.it = 25, xmax = FALSE, latlon = FALSE, na.rm = FALSE, quiet = FALSE)

Arguments

x

vector of length n representing the x coordinates (or longitude; see latlon).

y

vector of length n representing the y coordinates (or latitude).

z

vector of length n or matrix of dimension n x p representing p observation at each location.

w

an optional second variable with idenitical dimension to z (to estimate cross-correlograms).

df

degrees of freedom for the spline. Default is sqrt(n).

type

takes the value "boot" (default) to generate a bootstrap distribution or "perm" to generate a null distribution for the estimator

resamp

the number of resamples for the bootstrap or the null distribution.

npoints

the number of points at which to save the value for the spline function (and confidence envelope / null distribution).

save

if TRUE the whole matrix of output from the resampling is saved (an resamp x npoints dimensional matrix).

filter

if TRUE the Fourier filter method of Hall and coworkers is applied to ensure positive semidefiniteness of the estimator.

fw

if filter is TRUE, it may be useful to truncate the function at some distance w sets the truncation distance. when set to zero no truncation is done.

max.it

the maximum iteration for the Newton method used to estimate the intercepts.

xmax

if FALSE the max observed in the data is used. Otherwise all distances greater than xmax is omitted.

latlon

if TRUE, coordinates are latitude and longitude.

na.rm

if TRUE, NA's will be dealt with through pairwise deletion of missing values.

quiet

if TRUE the counter is supressed during execution.

Value

• An object of class "spline.correlog" is returned, consisting of the following components:
• real
  The list of estimates from the data.
• $x.intercept
  the lowest value at which the function is = 0. If correlation is initially negative, the distance is given as negative.
• $e.intercept
  the lowest value at which the function 1/e.
• $y.intercept
  the extrapolated value at x=0 (nugget).
• $predicted$x
  the x-axes for the fitted covariance function.
• $predcited$y
  the values for the covariance function.
• boot
  A list with the analogous output from the bootstrap or null distribution.
• $summary
  gives the full vector of output for the x.intercept, y.intercept, e.intercept, and a quantile summary for the resampling distribution.
• $boot
  if save=TRUE the full raw matrices from the resampling is saved.
• max.distance
  the maximum spatial distance considered.

Details

If observations are univariate the spline (cross-)correlogram represents the generalization of the spatial (cross-)correlogram; if observations are multivariate the spline (cross-)correlogram represents the generalization of the Mantel (cross-)correlogram. The spline (cross-)correlogram differes from the spatial correlogram (and Mantel correlogram) in that it estimated spatial dependence as a continous functions of distance (rather than binning into distance classes). The spline correlogram differs from the nonparametric (cross-)correlation function in that the zero-correlation reference line in the former corresponds to the regionwide correlation reference line in the latter. The x-intercept in the spline correlogram is the distance at which object are no more similar than that expected by-chance-alone across the region. Missing values are allowed -- values are assumed missing at random.

References

Bjornstad, O.N. & Falck, W. (2001) Nonparametric spatial covariance functions: estimation and testing. Environmental and Ecological Statistics, 8:53-70.

See Also

summary.spline.correlog plot.spline.correlog Sncf spline.correlog.2D correlog

Examples

#first generate some sample data
    x <- expand.grid(1:20, 1:5)[,1]
    y <- expand.grid(1:20, 1:5)[,2]

#z data from an exponential random field
    z <- cbind(
        rmvn.spa(x=x, y=y, p=2, method="exp"),
        rmvn.spa(x=x, y=y, p=2, method="exp")
        )

#w data from a gaussian random field
    w <- cbind(
        rmvn.spa(x=x, y=y, p=2, method="gaus"),
        rmvn.spa(x=x, y=y, p=2, method="gaus")
        )

#univariate spline correlogram
    fit1 <- spline.correlog(x=x, y=y, z=z[,1], resamp = 5)
    plot.spline.correlog(fit1)
    summary.spline.correlog(fit1)

#multivariate spline correlogram
    fit2 <- spline.correlog(x=x, y=y, z=z, resamp = 5)
    plot.spline.correlog(fit2)
    summary.spline.correlog(fit2)

#multivariate spline cross-correlogram
    fit3 <- spline.correlog(x=x, y=y, z=z, w=w, resamp = 5)
    plot.spline.correlog(fit3)
    summary.spline.correlog(fit3)