Given a response, set of locations, (optionally) a design matrix, and a specified covariance function, return the maximum Vecchia likelihood estimates, obtained with a Fisher scoring algorithm.
fit_model(
y,
locs,
X = NULL,
covfun_name = "matern_isotropic",
NNarray = NULL,
start_parms = NULL,
reorder = TRUE,
group = TRUE,
m_seq = c(10, 30),
max_iter = 40,
fixed_parms = NULL,
silent = FALSE,
st_scale = NULL,
convtol = 1e-04
)An object of class GpGp_fit, which is a list containing
covariance parameter estimates, regression coefficients,
covariance matrix for mean parameter estimates, as well as some other
information relevant to the model fit.
response vector
matrix of locations. Each row is a single spatial or spatial-temporal location. If using one of the covariance functions for data on a sphere, the first column should be longitudes (-180,180) and the second column should be latitudes (-90,90). If using a spatial-temporal covariance function, the last column should contain the times.
design matrix. Each row contains covariates for the corresponding
observation in y. If not specified, the function sets X to be a
matrix with a single column of ones, that is, a constant mean function.
string name of a covariance function.
See GpGp for information about supported covariance funtions.
Optionally specified array of nearest neighbor indices,
usually from the output of find_ordered_nn. If NULL,
fit_model will compute the nearest neighbors. We recommend that the user
not specify this unless there is a good reason to (e.g. if doing a comparison
study where one wants to control
NNarray across different approximations).
Optionally specified starting values for parameters.
If NULL,
fit_model will select default starting values.
TRUE/FALSE indicating whether maxmin ordering should be used
(TRUE) or whether no reordering should be done before fitting (FALSE).
If you want
to use a customized reordering, then manually reorder y, locs,
and X,
and then set reorder to FALSE. A random reordering is used
when nrow(locs) > 1e5.
TRUE/FALSE for whether to use the grouped version of the approximation (Guinness, 2018) or not. The grouped version is used by default and is always recommended.
Sequence of values for number of neighbors. By default,
a 10-neighbor
approximation is maximized, then a 30-neighbor approximation is
maximized using the
10 neighbor estimates as starting values.
However, one can specify any sequence
of numbers of neighbors, e.g. m_seq = c(10,30,60,90).
maximum number of Fisher scoring iterations
Indices of covariance parameters you would like to fix
at specific values. If you decide to fix any parameters, you must specify
their values in start_parms, along with the starting values for
all other parameters. For example, to fix the nugget at zero in
exponential_isotropic, set fixed_parms to c(3), and set
start_parms to c(4.7,3.1,0). The
last element of start_parms (the nugget parameter) is set to zero,
while the starting values for the other two parameters are 4.7 and 3.1.
TRUE/FALSE for whether to print some information during fitting.
Scaling for spatial and temporal ranges. Only applicable for
spatial-temporal models, where it is used in distance
calculations when selecting neighbors. st_scale must be specified
when covfun_name is a spatial-temporal covariance.
See Argo vignette for an example.
Tolerance for exiting the optimization.
Fisher scoring is stopped
when the dot product between the step and the gradient
is less than convtol.
fit_model is a user-friendly model fitting function
that automatically performs many of the auxiliary tasks needed for
using Vecchia's approximation, including reordering, computing
nearest neighbors, grouping, and optimization. The likelihoods use a small
penalty on small nuggets, large spatial variances,
and small smoothness parameter.
The Jason-3 windspeed vignette and the Argo temperature
vignette are useful sources for a
use-cases of the fit_model function for data on sphere.
The example below shows a very small example with a simulated dataset in 2d.
n1 <- 20
n2 <- 20
n <- n1*n2
locs <- as.matrix( expand.grid( (1:n1)/n1, (1:n2)/n2 ) )
covparms <- c(2,0.1,1/2,0)
y <- 7 + fast_Gp_sim(covparms, "matern_isotropic", locs)
X <- as.matrix( rep(1,n) )
## not run
# fit <- fit_model(y, locs, X, "matern_isotropic")
# fit
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