rlikfit: Likelihood Fit for Regoinalized Universal Kriging Model

Description Usage Arguments Details Value Author(s)

Description

Computes maximum likelihood estimates for parameters in a universal kriging model with regionally-varying covariance parameters.

Usage

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rlikfit(y, X, coords, reg.ind, cov.model = "exp", init.pars = NULL,
  optim.args = NULL)

Arguments

y

Dependent variable to be modeled

X

A n x d matrix of kriging covariates for the mean component.

coords

N x 2 matrix of coordinates

reg.ind

N-vector of distinct kriging regions. Defaults to reg.ind = rep(1,N), which yields traditional universal kriging.

cov.model

Either a single character string or a named vector providing the covariance model to be used. Valid values are "exp" and "iid". If only one value is provided, it is used for all regions.

init.pars

Vector of initial starting values for log-covariance parameters.

optim.args

List of named arguments passed to optim.

Details

The MLEs are obtained by maximizing the profile likelihood (see prof.rlik). By default, the opimization is done using the 'L-BFGS-B' method of optim.

If provided, the initial (log) parameters should be given as a vector of length 3 times the number of distinct regions. Values should follow the order of nugget, sill, and range for each region in succession. For example, if there are three regions the vector c(tau1, sigma1, rho1, tau2, sigma2, rho2, tau3, sigma3, rho3) should be given. If unspecifed, default initial values of 0 (on the log scale) are used. The default upper bound for the nugget and sill is log(10), and the default lower bound is log(0.0001). Default bounds for the range are log(0.001) and log(5000). These can be modified by providing 'upper' and 'lower' values in optim.args.

Regionally-varying coefficients for regression parameters are not explicitly implemented. However, they can be obtained by supplying the covariate matri X with suitable block structure.

Setting cov.model='iid' for all regions is equivalent to ordinary least squares regression, but this function is is not currently optimized for this use case and will likely be much slower and less precise than lm.

Value

An object of class 'rlikfit' containing:

log.cov.pars

maximized log-covariance parameters

beta

kriging regression covariate estimates

max.log.lik

maximized log-likelihood

hess.pd

indicator of positive definite hessian, if hess=TRUE

r

Number of regions

Author(s)

Joshua Keller, Paul Sampson


jpkeller/ruk documentation built on May 7, 2019, 4:40 p.m.