| loglik.GRF {geoR} | R Documentation |
This function computes the value of the log-likelihood for a Gaussian random field.
loglik.GRF(geodata, coords = geodata$coords, data = geodata$data,
obj.model = NULL, cov.model = "exp", cov.pars, nugget = 0,
kappa = 0.5, lambda = 1, psiR = 1, psiA = 0,
trend = "cte", method.lik = "ML", compute.dists = TRUE,
realisations = NULL)
geodata |
a list containing elements coords and
data as described next.
Typically an object of the class "geodata" - a geoR
data-set.
If not provided the arguments
coords and data must be provided instead. |
coords |
an n x 2 matrix, each row containing Euclidean
coordinates of the n data locations. By default it takes the
element coords of the argument geodata. |
data |
a vector with data values. By default it takes the
element data of the argument geodata. |
obj.model |
a object of the class variomodel with a fitted
model. Tipically an output of
likfit or variofit. |
cov.model |
a string specifying the model for the correlation
function. For further details see
documentation for cov.spatial. |
cov.pars |
a vector with 2 elements with values of the covariance parameters sigma^2 (partial sill) and phi (range parameter). |
nugget |
value of the nugget parameter. Defaults to 0. |
kappa |
value of the smoothness parameter. Defaults to 0.5. |
lambda |
value of the Box-Cox tranformation parameter. Defaults to 1. |
psiR |
value of the anisotropy ratio parameter. Defaults to 1, corresponding to isotropy. |
psiA |
value (in radians) of the anisotropy rotation parameter. Defaults to zero. |
trend |
specifies the mean part of the model.
The options are:
"cte" (constant mean),
"1st" (a first order polynomial
on the coordinates), "2nd" (a second order polynomial
on the coordinates), or a formula of the type ~X where X
is a matrix with the covariates (external trend). Defaults to "cte". |
method.lik |
options are "ML" for likelihood and "REML" for
restricted likelihood. Defaults to "ML". |
compute.dists |
for internal use with other function. Don't change the default unless you know what you are doing. |
realisations |
optional. A vector indicating replication number
for each data. For more details see as.geodata. |
The expression log-likelihood is:
l(theta) = -(n/2) * log(2 * pi) - 0.5 * log|V| - 0.5 * (y - F b)' V^{-1} (y - F b),
where n is the size of the data vector y, b is the mean (vector) parameter with dimention p, V is the covariance matrix and F is the matrix with the values of the covariates (a vector of 1's if the mean is constant.
The expression restricted log-likelihood is:
rl(theta) = -((n-p)/2) * log (2 * pi) + 0.5 * log |F'F| - 0.5 * log |V| - 0.5 * log |F'VF| - 0.5 * (y - Fb)' V^(-1) (y - Fb).
The numerical value of the log-likelihood.
Paulo Justiniano Ribeiro Jr. paulojus@leg.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.
Further information on the package geoR can be found at:
http://www.leg.ufpr.br/geoR.
likfit for likelihood-based parameter estimation.
loglik.GRF(s100, cov.pars=c(0.8, .25), nugget=0.2) loglik.GRF(s100, cov.pars=c(0.8, .25), nugget=0.2, met="RML") ## Computing the likelihood of a model fitted by ML s100.ml <- likfit(s100, ini=c(1, .5)) s100.ml s100.ml$loglik loglik.GRF(s100, obj=s100.ml) ## Computing the likelihood of a variogram fitted model s100.v <- variog(s100, max.dist=1) s100.vf <- variofit(s100.v, ini=c(1, .5)) s100.vf loglik.GRF(s100, obj=s100.vf)