NSconvo_fit {convoSPAT}  R Documentation 
Fit the nonstationary spatial model
Description
NSconvo_fit
estimates the parameters of the nonstationary
convolutionbased spatial model. Required inputs are the observed data and
locations. Optional inputs include mixture component locations (if not provided,
the number of mixture component locations are required), the fit radius,
the covariance model (exponential is the default), and whether or not the
nugget and process variance will be spatiallyvarying.
Usage
NSconvo_fit(
sp.SPDF = NULL,
coords = NULL,
data = NULL,
cov.model = "exponential",
mean.model = data ~ 1,
mc.locations = NULL,
N.mc = NULL,
lambda.w = NULL,
fixed.nugg2.var = NULL,
mean.model.df = NULL,
mc.kernels = NULL,
fit.radius = NULL,
ns.nugget = FALSE,
ns.variance = FALSE,
ns.mean = FALSE,
local.aniso = TRUE,
fix.tausq = FALSE,
tausq = 0,
fix.kappa = FALSE,
kappa = 0.5,
method = "reml",
print.progress = TRUE,
local.pars.LB = NULL,
local.pars.UB = NULL,
global.pars.LB = NULL,
global.pars.UB = NULL,
local.ini.pars = NULL,
global.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 
mc.locations 
Optional; matrix of mixture component locations. 
N.mc 
Optional; if 
lambda.w 
Scalar; tuning parameter for the weight function. Defaults to be the square of onehalf of the minimum distance between mixture component locations. 
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. 
mean.model.df 
Optional data frame; refers to the variables used
in 
mc.kernels 
Optional specification of mixture component kernel matrices (based on expert opinion, etc.). 
fit.radius 
Scalar; specifies the fit radius or neighborhood size for the local likelihood estimation. 
ns.nugget 
Logical; indicates if the nugget variance (tausq) should
be spatiallyvarying ( 
ns.variance 
Logical; indicates if the process variance (sigmasq)
should be spatiallyvarying ( 
ns.mean 
Logical; indicates if the mean coefficeints (beta)
should be spatiallyvarying ( 
local.aniso 
Logical; indicates if the local covariance should be
anisotropic ( 
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

method 
Indicates the estimation method, either maximum likelihood
( 
print.progress 
Logical; if 
local.pars.LB , local.pars.UB 
Optional vectors of lower and upper
bounds, respectively, used by the 
global.pars.LB , global.pars.UB 
Optional vectors of lower and upper
bounds, respectively, used by the 
local.ini.pars 
Optional vector of initial values used by the

global.ini.pars 
Optional vector of initial values used by the

Value
A "NSconvo" object, with the following components:
mc.locations 
Mixture component locations used for the simulated data. 
mc.kernels 
Mixture component kernel matrices used for the simulated data. 
MLEs.save 
Table of local maximum likelihood estimates for each mixture component location. 
kernel.ellipses 

data 
Observed data values. 
beta.GLS 
Generalized least squares estimates of beta,
the mean coefficients. For 
beta.cov 
Covariance matrix of the generalized least squares
estimate of beta. For 
Mean.coefs 
"Regression table" for the mean coefficient estimates,
listing the estimate, standard error, and tvalue (for 
tausq.est 
Estimate of tausq (nugget variance), either scalar (when

sigmasq.est 
Estimate of sigmasq (process variance), either scalar
(when 
beta.est 
Estimate of beta (mean coefficients), either a vector
(when 
kappa.MLE 
Scalar maximum likelihood estimate for kappa (when applicable). 
Cov.mat 
Estimated covariance matrix ( 
Cov.mat.chol 
Cholesky of 
cov.model 
String; the correlation model used for estimation. 
ns.nugget 
Logical, indicating if the nugget variance was estimated
as spatiallyvaring ( 
ns.variance 
Logical, indicating if the process variance was
estimated as spatiallyvarying ( 
fixed.nugg2.var 
N x N matrix with the fixed variance/covariance for the second (measurement error) nugget term (defaults to zero). 
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 
lambda.w 
Tuning parameter for the weight function. 
fix.kappa 
Logical, indicating if kappa was fixed ( 
kappa 
Scalar; fixed value of kappa. 
Examples
## Not run:
# Using white noise data
fit.model < NSconvo_fit( coords = cbind( runif(100), runif(100)),
data = rnorm(100), fit.radius = 0.4, N.mc = 4 )
## End(Not run)