maxlik.cov.sp | R Documentation |
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.
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")
X |
A numeric matrix of size |
y |
A vector of length |
coords |
A numeric matrix of size |
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 |
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 |
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 |
upper |
A vector giving upper bounds for the covariance parameters |
control |
A list giving tuning parameters for the |
optimizer |
A vector describing the optimization function to use for the optimization. Currently, only |
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]
.
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 |
convergence |
Convergence message from |
message |
Message from |
iterations |
Number of iterations for optimization to converge. |
evaluations |
Evaluations from |
Joshua French
cov.st
#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)
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