correlog.nc {ncf}

Non-centered spatial (cross-)correlogram

Description

correlog.nc is the function to estimate the non-centered (cross-)correlogram. The non-centered correlogram provides estimates of the spatial correlation for discrete distance classes. The function requires multiple observations at each location (use correlog otherwise).

Usage

correlog.nc(
  x,
  y,
  z,
  w = NULL,
  increment,
  resamp = 999,
  na.rm = FALSE,
  latlon = 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

a matrix of dimension n x p representing p (>1) observation at each location.

w

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

increment

increment for the uniformly distributed distance classes.

resamp

the number of permutations under the null to assess level of significance.

na.rm

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

latlon

If TRUE, coordinates are latitude and longitude.

quiet

If TRUE, the counter is suppressed during execution.

Details

The non-centered correlogram estimates spatial dependence at discrete distance classes. The method corresponds to the modified correlogram of Koenig & Knops(1998), but augmented to potentially estimate the cross-correlogram). The function requires multiple observations at each location. Missing values is allowed in the multivariate case (pairwise deletion will be used).

Missing values are allowed – values are assumed missing at random.

Value

An object of class "correlog" is returned, consisting of the following components:

correlation

the value for the Moran (or Mantel) similarity.

mean.of.class

the actual average of the distances within each distance class.

nlok

the number of pairs within each distance class.

x.intercept

the interpolate x.intercept of Epperson (1993).

p

the permutation p-value for each distance-class.

corr0

If a cross-correlogram is calculated, corr0 gives the empirical within-patch cross-correlation.

Author(s)

Ottar N. Bjornstad [e-mail]

References

Bjornstad, O.N., Ims, R.A. & Lambin, X. (1999) Spatial population dynamics: Analysing patterns and processes of population synchrony. Trends in Ecology and Evolution, 11, 427-431. <doi:10.1016/S0169-5347(99)01677-8>

Koenig, W.D. & Knops, J.M.H. (1998) Testing for spatial autocorrelation in ecological studies. Ecography, 21, 423-429. <doi:10.1111/j.1600-0587.1998.tb00407.x>

See Also

plot.correlog, 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")
  )

# noncentered (Mantel) correlogram 
fit1 <- correlog.nc(x = x, y = y, z = z, increment = 2, resamp = 499)
## Not run: plot(fit1)