spline.correlog: Uni- and multivariate spline correlograms
In ncf: Spatial Covariance Functions

spline.correlog

R Documentation

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 identical 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
`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 (a 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 fw 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 suppressed during execution.

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 differs from the spatial correlogram (and Mantel correlogram) in that it estimated spatial dependence as a continuous 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 region-wide 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.

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.

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Bjornstad, O.N. & Falck, W. (2001) Nonparametric spatial covariance functions: estimation and testing. Environmental and Ecological Statistics, 8:53-70. <doi:10.1023/A:1009601932481>

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 = 100)
## Not run: plot.spline.correlog(fit1)
summary(fit1)

# multivariate spline correlogram
fit2 <- spline.correlog(x = x, y = y, z = z, resamp = 100)
## Not run: plot.spline.correlog(fit2)
summary(fit2)

# multivariate spline cross-correlogram
fit3 <- spline.correlog(x = x, y = y, z = z, w = w, resamp = 100)
## Not run: plot.spline.correlog(fit3)
summary(fit3)

ncf documentation built on May 7, 2022, 5:05 p.m.