SpatialTools: maxlik.cov.sp – R documentation

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maxlik.cov.sp

Determines maximum likelihood estimates of covariance parameters

Description

Estimates covariance parameters of spatial covariance functions using maximum likelihood or restricted maximum likelihood. See cov.sp for more details of covariance functions to be estimated.

Usage

maxlik.cov.sp(X, y, coords, sp.type = "exponential", 
	    range.par = stop("specify range.par argument"), 
	    error.ratio = stop("specify error.ratio argument"), 
	    smoothness = 0.5,  
	    D = NULL, reml = TRUE, lower = NULL, upper = NULL, 
	    control = list(trace = TRUE), optimizer="nlminb")

Arguments

`X`	A numeric matrix of size n \times k containing the design matrix of the data locations.
`y`	A vector of length n containing the observed responses.
`coords`	A numeric matrix of size n \times d containing the locations of the observed responses.
`sp.type`	A character vector specifying the spatial covariance type. Valid types are currently exponential, gaussian, matern, and spherical.
`range.par`	An initial guess for the spatial dependence parameter.
`error.ratio`	A value non-negative value indicating the ratio `error.var/sp.par[1]`.
`smoothness`	A positive number indicating the smoothness of the matern covariance function, if applicable.
`D`	The Euclidean distance matrix for the coords matrix. Must be of size n \times n.
`reml`	A boolean value indicating whether restricted maximum likelihood estimation should be used. Defaults to TRUE.
`lower`	A vector giving lower bounds for the covariance parameters `sp.par[2]`, `error.ratio`, and `smoothness` (when the model is matern). Order matters! If not given defaults to an upper bound of Inf for `sp.par[2]`, 1 for `error.ratio`, and 10 for `smoothness`.
`upper`	A vector giving upper bounds for the covariance parameters `sp.par[2]`, `error.ratio`, and `smoothness` (when the model is matern). Order matters! If not given defaults to an upper bound of Inf for `sp.par[2]`, 1 for `error.ratio`, and 10 for `smoothness`.
`control`	A list giving tuning parameters for the `nlminb` function. See `nlminb` for more details.
`optimizer`	A vector describing the optimization function to use for the optimization. Currently, only `nlminb` is an acceptable value.

Details

When doing the numerical optimizaiton, the covariance function is reparameterized slightly to speedup computation. Specifically, the variance parameter for the process of interest,sp.par[1], is profiled out, and the error.var parameter is parameterized as sp.par[1] * error.ratio, where error.ratio = error.var/sp.par[1].

Value

Returns a list with the following elements:

`sp.type`	The covariance form used.
`sp.par`	A vector containing the estimated variance of the hidden process and the spatial dependence.
`error.var`	The estimated error variance.
`smoothness`	The smoothness of the matern covariance function.
`par`	The final values of the optimization parameters. Note that these will not necessarily match `sp.par`, `error.var`, and `smoothness` because of the reparameterization.
`convergence`	Convergence message from `nlminb`.
`message`	Message from `nlminb`.
`iterations`	Number of iterations for optimization to converge.
`evaluations`	Evaluations from `nlminb`.

Author(s)

Joshua French

Examples

#generate 20 random (x, y) coordinates
coords <- matrix(rnorm(20), ncol = 2)

#create design matrix
X <- cbind(1, coords)

#create mean for observed data to be generated
mu <- X %*% c(1, 2, 3)

#generate covariance matrix
V <- exp(-dist1(coords))

#generate observe data
y <- rmvnorm(mu = mu, V = V)

#find maximum likelihood estimates of covariance parameters
maxlik.cov.sp(X = X, y = y, coords = coords,
    sp.type = "exponential", range.par = 1, error.ratio = 0, 
    reml = TRUE)

SpatialTools

Tools for Spatial Data Analysis

v1.0.4

GPL (>= 2)

Authors

Joshua French <joshua.french@ucdenver.edu>

Initial release