Aniso_fit {convoSPAT}  R Documentation 
Fit the stationary spatial model
Description
Aniso_fit
estimates the parameters of the stationary spatial model.
Required inputs are the observed data and locations.
Optional inputs include the covariance model (exponential is the default).
Usage
Aniso_fit(
sp.SPDF = NULL,
coords = NULL,
data = NULL,
cov.model = "exponential",
mean.model = data ~ 1,
fixed.nugg2.var = NULL,
method = "reml",
fix.tausq = FALSE,
tausq = 0,
fix.kappa = FALSE,
kappa = 0.5,
local.pars.LB = NULL,
local.pars.UB = NULL,
local.ini.pars = NULL
)
Arguments
sp.SPDF 
A " 
coords 
An N x 2 matrix where each row has the twodimensional coordinates of the N data locations. 
data 
A vector or matrix with N rows, containing the data values. Inputting a vector corresponds to a single replicate of data, while inputting a matrix corresponds to replicates. In the case of replicates, the model assumes the replicates are independent and identically distributed. 
cov.model 
A string specifying the model for the correlation
function; defaults to 
mean.model 
An object of class 
fixed.nugg2.var 
Optional; describes the variance/covariance for a fixed (second) nugget term (represents a known error term). Either a vector of length N containing a stationspecific variances (implying independent error) or an NxN covariance matrix (implying dependent error). Defaults to zero. 
method 
Indicates the estimation method, either maximum likelihood
( 
fix.tausq 
Logical; indicates whether the default nugget term
(tau^2) should be fixed ( 
tausq 
Scalar; fixed value for the nugget variance (when

fix.kappa 
Logical; indicates if the kappa parameter should be
fixed ( 
kappa 
Scalar; value of the kappa parameter. Only used if

local.pars.LB , local.pars.UB 
Optional vectors of lower and upper
bounds, respectively, used by the 
local.ini.pars 
Optional vector of initial values used by the

Value
A list with the following components:
MLEs.save 
Table of local maximum likelihood estimates for each mixture component location. 
data 
Observed data values. 
beta.GLS 
Vector of generalized least squares estimates of beta, the mean coefficients. 
beta.cov 
Covariance matrix of the generalized least squares estimate of beta. 
Mean.coefs 
"Regression table" for the mean coefficient estimates, listing the estimate, standard error, and tvalue. 
Cov.mat 
Estimated covariance matrix ( 
Cov.mat.chol 
Cholesky of 
aniso.pars 
Vector of MLEs for the anisotropy parameters lam1, lam2, eta. 
aniso.mat 
2 x 2 anisotropy matrix, calculated from

tausq.est 
Scalar maximum likelihood estimate of tausq (nugget variance). 
sigmasq.est 
Scalar maximum likelihood estimate of sigmasq (process variance). 
kappa.MLE 
Scalar maximum likelihood estimate for kappa (when applicable). 
fixed.nugg2.var 
N x N matrix with the fixed variance/covariance for the second (measurement error) nugget term (defaults to zero). 
cov.model 
String; the correlation model used for estimation. 
coords 
N x 2 matrix of observation locations. 
global.loglik 
Scalar value of the maximized likelihood from the global optimization (if available). 
Xmat 
Design matrix, obtained from using 
fix.kappa 
Logical, indicating if kappa was fixed ( 
kappa 
Scalar; fixed value of kappa. 
Examples
## Not run:
# Using iid standard Gaussian data
aniso.fit < Aniso_fit( coords = cbind(runif(100), runif(100)),
data = rnorm(100) )
## End(Not run)