covariog {geoRglm} | R Documentation |
Computes the sample empirical (sample) covariogram described in Christensen, Moller and Waagepetersen (2000).
Output is returned as a binned covariogram
. The function is NOT
a general function for computing the covariogram, and it is in fact of
very limited use.
covariog(geodata, coords = geodata$coords, data = geodata$data, units.m = "default", uvec = "default", bins.lim = "default", estimator.type = c("poisson", "not-poisson"), max.dist = NULL, pairs.min = 2)
geodata |
a list containing elements data and coords
as described next. Typically an object of the class
"geodata" - a geoR data set.
If not provided the arguments data and
coords must be provided instead.
The list may also contain an argument units.m as described below.
|
coords |
an n x 2 matrix containing
coordinates of the n data locations in each row.
Default is geodata$coords , if provided.
|
data |
a vector or matrix with data values.
If a matrix is provided, each column is regarded as one variable or realization.
Default is geodata$data , if provided.
|
units.m |
n-dimensional vector of observation times for the data. By default (units.m = "default" ),
it takes geodata$units.m in case this exist and else a vector of 1's. |
uvec |
a vector with values defining the covariogram binning. The
values of uvec defines the midpoints of the bins.If uvec[1] > 0 the first bin is: 0 < u <= uvec[2] - 0.5*(uvec[2] - uvec[1]). If uvec[1] = 0 first bin is: 0 < u <= 0.5*uvec[2], and uvec[1] is replaced by the midpoint of this interval. The default ( uvec = "default" ) is that
uvec[i]=max.dist*(i-1)/14 for i=1,...,15.
|
bins.lim |
separating values for the binning. By default these values are defined via the argument of
uvec . |
estimator.type |
"poisson" estimates the value hat{C}(0) using the
Poisson assumption. "not-poisson" doesn't compute hat{C}(0).
|
max.dist |
a number defining the maximal distance for the covariogram. Pairs of locations separated by a larger distance than this value are ignored in the covariogram calculation. Default is the maximum distance between pairs of data locations. |
pairs.min |
An integer number defining the minimum number of pairs for the bins. Bins with number of pairs smaller than this value are ignored. |
Covariograms can be used in geostatistical analysis for exploratory purposes, to estimate covariance parameters and/or to compare theoretical and fitted models against the empirical covariogram.
The covariogram computed by this function assumes a specific model, a spatial GLMM, and furthermore it assumes that the link-function is the logarithm (i.e. it should not be used for the binomial-logistic model !).
Assume that the conditional distribution of Y_i given S_i
has mean t_i*exp(S_i), where the values of t_i are given in units.m
.
The estimator implemented is
hat{C}(u) = log(frac{1/|W_u^{Delta}|sum_{(i,j) in W_u^{Delta}} Y(x_i)*Y(x_j) /(t_i*t_j)}{(1/n sum_i Y(x_i)/t_i)^2}), u > 0
When a Poisson distribution is assumed, then
hat{C}(0) = log(frac{1/n sum_i Y(x_i)*(Y(x_i)-1)/t_i^2}{(1/n sum_i Y(x_i)/t_i)^2}).
An object of the class
covariogram
which is a
list with the following components:
u |
a vector with distances. |
v |
a vector with estimated covariogram values at distances given
in u . When estimator.type = "poisson" , the first value in v is the estimate of sigma^2,
hat{C}(0). |
n |
number of pairs in each bin. When estimator.type = "poisson" , the first value in n is v0 . |
v0 |
the estimate of sigma^2, hat{C}(0). |
bins.lim |
Separating values for the binning provided in the function call. |
estimator.type |
echoes the type of estimator used. |
call |
The function call. |
Ole F. Christensen OleF.Christensen@agrsci.dk,
Paulo J. Ribeiro Jr. Paulo.Ribeiro@est.ufpr.br.
Christensen, O. F., Moller, J. and Waagepetersen R. (2000). Analysis of spatial data using generalized linear mixed models and Langevin-type Markov chain Monte Carlo. Research report R-00-2009, Aalborg University.
Further information about geoRglm can be found at:
http://www.daimi.au.dk/~olefc/geoRglm.
covariog.model.env
for
covariogram envelopes and plot.covariogram
for graphical
output.
data(p50) covar <- covariog(p50, uvec=c(1:10)) plot(covar) ## Now excluding the bin at zero (only assuming log-link). covar2 <- covariog(p50,uvec=c(1:10), estimator.type="no") plot(covar2)