Aniso_fit: Fit the stationary spatial model

In markdrisser/convoSPAT: Convolution-Based Nonstationary Spatial Modeling

Description

Aniso_fit estimates the parameters of the stationary spatial model. Required inputs are the observed data and locations (a geoR object with $coords and $data). Optional inputs include the covariance model (exponential is the default).

Usage

Aniso_fit(geodata = NULL, sp.SPDF = NULL, coords = geodata$coords,
  data = geodata$data, 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

geodata	A list containing elements coords and data as described next. Typically an object of the class "geodata", although a geodata object only allows data to be a vector (no replicates). If not provided, the arguments coords and data must be provided instead.
sp.SPDF	A "SpatialPointsDataFrame" object, which contains the spatial coordinates and additional attribute variables corresponding to the spatoal coordinates
coords	An N x 2 matrix where each row has the two-dimensional coordinates of the N data locations. By default, it takes the coords component of the argument geodata, if provided.
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; following geoR, defaults to "exponential". Options available in this package are: "exponential", "cauchy", "matern", "circular", "cubic", "gaussian", "spherical", and "wave". For further details, see documentation for cov.spatial.
mean.model	An object of class formula, specifying the mean model to be used. Defaults to an intercept only.
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 station-specific variances (implying independent error) or an NxN covariance matrix (implying dependent error). Defaults to zero.
method	Indicates the estimation method, either maximum likelihood ("ml") or restricted maximum likelihood ("reml").
fix.tausq	Logical; indicates whether the default nugget term (tau^2) should be fixed (TRUE) or estimated (FALSE). Defaults to FALSE.
tausq	Scalar; fixed value for the nugget variance (when fix.tausq = TRUE).
fix.kappa	Logical; indicates if the kappa parameter should be fixed (TRUE) or estimated (FALSE). Defaults to FALSE (only valid for cov.model = "matern" and cov.model = "cauchy").
kappa	Scalar; value of the kappa parameter. Only used if fix.kappa = TRUE.
local.pars.LB, local.pars.UB	Optional vectors of lower and upper bounds, respectively, used by the "L-BFGS-B" method option in the optim function for the local parameter estimation. Each vector must be of length five, containing values for lam1, lam2, tausq, sigmasq, and nu. Default for local.pars.LB is rep(1e-05,5); default for local.pars.UB is c(max.distance/2, max.distance/2, 4*resid.var, 4*resid.var, 100), where max.distance is the maximum interpoint distance of the observed data and resid.var is the residual variance from using lm with mean.model.
local.ini.pars	Optional vector of initial values used by the "L-BFGS-B" method option in the optim function for the local parameter estimation. The vector must be of length five, containing values for lam1, lam2, tausq, sigmasq, and nu. Defaults to c(max.distance/10, max.distance/10, 0.1*resid.var, 0.9*resid.var, 1), where max.distance is the maximum interpoint distance of the observed data and resid.var is the residual variance from using lm with mean.model.

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 t-value.
Cov.mat	Estimated covariance matrix (N.obs x N.obs) using all relevant parameter estimates.
Cov.mat.chol	Cholesky of Cov.mat (i.e., chol(Cov.mat)), the estimated covariance matrix (N.obs x N.obs).
aniso.pars	Vector of MLEs for the anisotropy parameters lam1, lam2, eta.
aniso.mat	2 x 2 anisotropy matrix, calculated from aniso.pars.
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 lm with mean.model.
fix.kappa	Logical, indicating if kappa was fixed (TRUE) or estimated (FALSE).
kappa	Scalar; fixed value of kappa.

Examples

# Using iid standard Gaussian data
aniso.fit <- Aniso_fit( coords = cbind(runif(100), runif(100)),
data = rnorm(100) )

markdrisser/convoSPAT documentation built on May 21, 2019, 11:48 a.m.