| fitGLS_opt {remotePARTS} | R Documentation |
Fit a PARTS GLS model, with maximum likelihood spatial parameters
Description
Fit a PARTS GLS model, with maximum likelihood spatial parameters
Usage
fitGLS_opt(
formula,
data = NULL,
coords,
distm_FUN = "distm_scaled",
covar_FUN = "covar_exp",
start = c(range = 0.01, nugget = 0),
fixed = c(),
opt.only = FALSE,
formula0 = NULL,
save.xx = FALSE,
save.invchol = FALSE,
no.F = TRUE,
trans = list(),
backtrans = list(),
debug = TRUE,
ncores = NA,
...
)
Arguments
formula |
a model formula, passed to |
data |
an optional data frame environment in which to search for
variables given by |
coords |
a numeric coordinate matrix or data frame, with two columns and rows corresponding to each pixel |
distm_FUN |
a function to calculate a distance matrix from |
covar_FUN |
a function to estimate distance-based covariances |
start |
a named vector of starting values for each parameter to be estimated;
names must match the names of arguments in |
fixed |
an optional named vector of fixed parameter values; names
must match the names of arguments in |
opt.only |
logical: if TRUE, execution will halt after estimating the parameters; a final GLS will not be fit with the estimated parameters |
formula0, save.xx, save.invchol, no.F |
arguments passed to |
trans |
optional list of functions for transforming the values in
|
backtrans |
optional list of functions for back-transforming parameters
to their correct scale (for use with |
debug |
logical: debug mode (for use with |
ncores |
an optional integer indicating how many CPU threads to use for calculations. |
... |
additional arguments passed to |
Details
Estimate spatial parameters, via maximum likelihood, from data rather than from time series residuals; Fit a GLS with these specifications.
fitGLS_opt fits a GLS by estimating spatial parameters from
data. fitCor, combined with fitGLS(nugget = NA),
gives better estimates of spatial parameters, but time-series residuals may
not be available in all cases. In these cases, spatial parameters can be
estimated from distances among points and a response vector. Mathematical
optimization of the log likelihood of different GLS models are computed by
calling optim() on fitGLS.
Distances are calculated with distm_FUN and a covariance matrix is
calculated from these distances with covar_FUN. Arguments to to
covar_FUN, except distances, are given by start and fixed.
Parameters specified in start will be be estimated while those given
by fixed will remain constant throughout fitting. Parameter names in
start and fixed should exactly match the names of arguments in
covar_FUN and should not overlap (though, fixed takes precedence).
In addition to arguments of covar_FUN a "nugget" component can
also be occur in start or fixed. If "nugget" does not occur
in either vector, the GLS are fit with nugget = 0. A zero nugget also
allows much faster computation, through recycling the common
inverse cholesky matrix in each GLS computation. A non-zero nugget requires
inversion of a different matrix at each iteration, which can be
substantially slower.
If opt.only = FALSE, the estimated parameters are used to fit the final
maximum likelihood GLS solution with fitGLS() and arguments
formula0, save.xx, save.invchol, and no.F.
Some parameter combinations may not produce valid covariance matrices. During
the optimization step messages about non-positive definitive V may result on
some iterations. These warnings are produced by fitGLS and NA
log-likelihoods are returned in those cases.
Note that fitGLS_opt fits multiple GLS models, which requires
inverting a large matrix for each one (unless a fixed 0 nugget is used).
This process is very computationally intensive and may take a long time to
finish depending upon your machine and the size of the data.
Sometimes optim can have a difficult time finding a reasonable solution
and without any constraits on parameter space (with certain algorithms), results
may even be nonsensical. To combat this, fitGLS_opt has the arguments
trans and backtrans which allow you to transform
(and back-transform) parameters to a different scale. For example, you may
want to force the 'range' parameter between 0 and 1. The logit function can
do just that, as its limits are -Inf and Inf as x approaches 0 and 1,
respectively. So, we can set trans to the logit function:
trans = list(range = function(x)log(x/(1-x))). Then we need to set
backtrans to the inverse logit function to return a parameter value
between 0 and 1: backtrans = list(range = function(x)1/(1+exp(-x))).
This will force the optimizer to only search for the range parameter in the
space from 0 to 1. Any other constraint function can be used for trans
provided that there is a matching back-transformation.
Value
If opt.only = TRUE, fitGLS_opt returns the
output from stats::optim(): see it's documentation for more details.
Otherwise, a list with two elements is returned:
- opt
output from
optim, as above- GLS
a "remoteGLS" object. See
fitGLSfor more details.
See Also
fitCor for estimating spatial parameters from time
series residuals; fitGLS for fitting GLS and with the option
of estimating the maximum-likelihood nugget component only.
Examples
## read data
data(ndvi_AK10000)
df = ndvi_AK10000[seq_len(200), ] # first 200 rows
## estimate nugget and range (very slow)
fitGLS_opt(formula = CLS_coef ~ 0 + land, data = df,
coords = df[, c("lng", "lat")], start = c(range = .1, nugget = 0),
opt.only = TRUE)
## estimate range only, fixed nugget at 0, and fit full GLS (slow)
fitGLS_opt(formula = CLS_coef ~ 0 + land, data = df,
coords = df[, c("lng", "lat")],
start = c(range = .1), fixed = c("nugget" = 0),
method = "Brent", lower = 0, upper = 1)
## constrain nugget to 0 and 1
logit <- function(p) {log(p / (1 - p))}
inv_logit <- function(l) {1 / (1 + exp(-l))}
fitGLS_opt(formula = CLS_coef ~ 0 + land, data = df,
coords = df[, c("lng", "lat")],
start = c(range = .1, nugget = 1e-10),
trans = list(nugget = logit), backtrans = list(nugget = inv_logit),
opt.only = TRUE)