ngme.spatial: Parameter estimation of non-Gaussian spatial models.

In davidbolin/ngme: Linear Mixed Effects Models With Flexible Distributions

Parameter estimation of non-Gaussian spatial models.

Description

Likelihood-based parameter estimation of spatial non-Gaussian models.

Usage

ngme.spatial(
  fixed,
  random = NULL,
  fixed2 = NULL,
  random2 = NULL,
  group.id = NULL,
  use.process = TRUE,
  reffects = "Normal",
  process = c("Normal", "matern"),
  error = "Normal",
  error_assymetric = FALSE,
  data,
  location.names = NULL,
  silent = TRUE,
  nIter = 1000,
  mesh = NULL,
  controls = list(learning.rate = 0.3, polyak.rate = -1, nBurnin = 100, nSim = 2,
    pSubsample = NULL, nPar.burnin = 0, step0 = 1, alpha = 0.3, nBurnin.learningrate =
    NULL, nBurnin.base = 0, subsample.type = 1, pSubsample2 = 0.3, individual.sigma =
    FALSE, iter.start = 0),
  controls.init = list(learning.rate.init = 0.9, polyak.rate.init = -1, nBurnin.init =
    100, nSim.init = 2, nIter.init = 1000, pSubsample.init = 0.1, nPar.burnin.init = 0,
    step0.init = 0.9, alpha.init = 0.6, nBurnin.learningrate.init = NULL,
    nBurnin.base.init = 0, subsample.type.init = 0, pSubsample2.init = 0.3,
    individual.sigma.init = FALSE),
  init.fit = NULL,
  debug = FALSE
)

Arguments

fixed	A two-sided formula to specify the fixed effects design matrix.
random	A one-sided formula to specify the random effects design matrix (if any).
fixed2	A two-sided formula to specify the fixed effects design matrix for the second dimension for bivariate models.
random2	A one-sided formula to specify the random effects design matrix (if any) for the second dimension for bivariate models.
use.process	A logical variable for inclusion of the stochastic process in the mixed model. Default is "TRUE".
reffects	A character string that indicates the distribution of the random effects if present in the model. Available options are: "Normal" for Normal distribution, and "NIG" for Normal-inverse Gaussian.
process	A character string specifying the distribution of the driving noise of the spatial process Available options are first are: "Normal" for Normal distribution, "NIG" for Normal-inverse Gaussian, "GAL" for generalised-asymmetric Laplace, and "CH" for Cauchy. For multivariate models, only "Normal" and "NIG" are currently available.
error	A character string to specify the distribution of the error term. Available options are: "Normal" for Normal distribution, "NIG" for Normal-inverse Gaussian, "tdist" for t. For mulivariatae models, only "Normal" is currently available.
error_assymetric	if true the non-Gaussian error is assymetric
data	A data-frame from which the response and covariates to be extracted.
location.names	A character vector with the names of the spatial coordinates.
silent	A logical value for printing the details of the iterations; "TRUE" indicates do not print, "FALSE" print.
nIter	A numeric value for the number of iteration that will be used by the stochastic gradient.
mesh	A mesh object of class inla.mesh
controls	A list of control variables for parameter estimation. See ngme for details.
controls.init	A list of control variables to be used to fit the normal model to get the initial values for fitting a model with at least one of random effects, process and error being non-Gaussian. See ngme for details.
init.fit	A fitted ngme.spatial object to be used as a starting value for estimation.

Details

The model that is estimated is of the form

Y_{ij} = B(s_i)beta + U(s_i)beta_j + X_j(s_i) + e_{ij}

Here i denots the index of the spatial location for the measurement and j denotes the number of the replicate in case of repeated measurements. The common mean value B(s_i)beta is specified using fixed effects, and the random effect part U(s_i)beta_j specifies a mean value varying between replicates. The process X_j(s) is a spatial process (independent between replicates) with a Matern covariance structure, specified as a stochastic PDE with possibly non-Gaussian driving noise. The measurement noise e_{ij} is assumed to be independent between observations and replicates.

Value

A list of outputs.

See Also

predict.ngme.spatial

davidbolin/ngme documentation built on Dec. 5, 2023, 11:48 p.m.