Sncf {ncf} | R Documentation |
Sncf is the function to estimate the nonparametric (cross-)correlation
function using a smoothing spline as an equivalent kernel. The function
requires multiple observations at each location (use spline.correlog
otherwise).
Sncf(x, y, z, w = NULL, df = NULL, type = "boot", resamp = 1000, npoints = 300, save = FALSE, filter = FALSE, fw = 0, max.it = 25, xmax = FALSE, na.rm = FALSE, latlon = FALSE, circ = FALSE, quiet = FALSE)
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 |
matrix of dimension n x p representing p observation at each location. |
w |
an optional second matrix of dimension n x p for species 2 (to estimate the spatial cross-correlation function). |
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. (more work may be needed on this.) |
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. |
na.rm |
if TRUE, NA's will be dealt with through pairwise deletion of missing values for each pair of time series – it will dump if any one pair has less than two (temporally) overlapping observations. |
latlon |
if TRUE, coordinates are latitude and longitude. |
circ |
if TRUE, the observations are assumed to be angular (in radians), and circular correlation is used. |
quiet |
if TRUE the counter is supressed during execution. |
Missing values are allowed – values are assumed missing at random.
The circ argument computes a circular version of the Pearson's product
moment correlation (see cor2
). This option is to calculate
the 'nonparametric phase coherence function' (Grenfell et al. 2001)
An object of class "Sncf" is returned, consisting of the following components:
real |
The list of estimates from the data. |
$cbar |
the regional average correlation. |
$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). |
$cbar.intercept |
distance at which regional average correlation is reach. |
$predicted$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, cbar.intercept, cbar 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. |
Ottar N. Bjornstad onb1@psu.edu
Hall, P. & Patil, P. (1994) Properties of nonparametric estimators of autocovariance for stationary random fields. Probability Theory and Related Fields, 99:399-424.
Hall, P., Fisher, N.I. & Hoffmann, B. (1994) On the nonparametric estimation of covariance functions. Annals of Statistics, 22:2115-2134.
Bjornstad, O.N. & Falck, W. (2001) Nonparametric spatial covariance functions: estimation and testing. Environmental and Ecological Statistics, 8:53-70.
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.
Bjornstad, O. N., and J. Bascompte. (2001) Synchrony and second order spatial correlation in host-parasitoid systems. Journal of Animal Ecology 70:924-933.
Grenfell, B.T., Bjornstad, O.N., & Kappey, J. (2001) Travelling waves and spatial hierarchies in measles epidemics. Nature 414:716-723.
summary.Sncf
plot.Sncf
Sncf2D
Sncf.srf
#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") ) #multivariate nonparametric covariance function fit1 <- Sncf(x=x, y=y, z=z, resamp = 5) ## Not run: plot.Sncf(fit1) summary.Sncf(fit1) #multivariate nonparametric cross-covariance function fit2 <- Sncf(x=x, y=y, z=z, w=w, resamp = 5) ## Not run: plot.Sncf(fit2) summary.Sncf(fit2)