Lik {GeoModels}

Optimizes the Log Likelihood

Description

Subroutine called by GeoFit. The procedure estimates the model parameters by maximization of the log-likelihood.

Usage

Lik(copula,bivariate,coordx,coordy,coordt,
coordx_dyn,corrmodel,data,fixed,flagcor,flagnuis,
           grid,lower,mdecomp,model,namescorr,
           namesnuis,namesparam,numcoord,
           numpairs,numparamcor,numtime,optimizer,
           onlyvar,parallel,param,radius,setup,
           spacetime,sparse,varest,taper,type,
           upper,ns,X,neighb,MM,aniso)

Arguments

copula

String; the type of copula. It can be "Beta" or "Gaussian"

bivariate

Logical; if TRUE then the data come froma a bivariate random field. Otherwise from a univariate random field.

coordx

A numeric (d \times 2)-matrix (where d is the number of spatial sites) assigning 2-dimensions of spatial coordinates or a numeric d-dimensional vector assigning 1-dimension of spatial coordinates.

coordy

A numeric vector assigning 1-dimension of spatial coordinates; coordy is interpreted only if coordx is a numeric vector or grid=TRUE otherwise it will be ignored. Optional argument, the default is NULL then coordx is expected to be numeric a (d \times 2)-matrix.

coordt

A numeric vector assigning 1-dimension of temporal coordinates. Optional argument, the default is NULL then a spatial random field is expected.

coordx_dyn

A list of m numeric (d_t \times 2)-matrices containing dynamical (in time) spatial coordinates. Optional argument, the default is NULL

corrmodel

Numeric; the id of the correlation model.

data

A numeric vector or a (n \times d)-matrix or (d \times d \times n)-matrix of observations.

flagcor

A numeric vector of flags denoting which correlation parameters have to be estimated.

flagnuis

A numeric verctor of flags denoting which nuisance parameters have to estimated.

fixed

A numeric vector of parameters that will be considered as known values.

grid

Logical; if FALSE (the default) the data are interpreted as a vector or a (n \times d)-matrix, instead if TRUE then (d \times d \times n)-matrix is considered.

lower

An optional named list giving the values for the lower bound of the space parameter when the optimizer is L-BFGS-B or nlminb or optimize. The names of the list must be the same of the names in the start list.

model

Numeric; the id value of the density associated to the likelihood objects.

namescorr

String; the names of the correlation parameters.

namesnuis

String; the names of the nuisance parameters.

namesparam

String; the names of the parameters to be maximised.

numcoord

Numeric; the number of coordinates.

numpairs

Numeric; the number of pairs.

numparamcor

Numeric; the number of the correlation parameters.

numtime

Numeric; the number of temporal observations.

mdecomp

String; the type of matrix decomposition used in the simulation. Default is cholesky. The other possible choices is svd (Singular values decomposition).

optimizer

String; the optimization algorithm (see optim for details). Nelder-Mead is the default. Other possible choices are nlm, BFGS L-BFGS-B and nlminb. In these last two cases upper and lower bounds can be passed by the user. In the case of one-dimensional optimization, the function optimize is used.

onlyvar

Logical; if TRUE (and varest is TRUE) only the variance covariance matrix is computed without optimizing. FALSE is the default.

parallel

Logical; if TRUE optmization is performed using optimParallel using the maximum number of cores, when optimizer is L-BFGS-B.FALSE is the default.

param

A numeric vector of parameters.

sparse

Logical; if TRUE then maximum likelihood is computed using sparse matrices algorithms.FALSE is the default.

radius

Numeric; the radius of the sphere when considering data on a sphere.

ns

Numeric: vector of number of location sites for each temporal instants

setup

A List of useful components for the estimation based on the maximum tapered likelihood.

spacetime

Logical; if the random field is spatial (FALSE) or spatio-temporal (TRUE).

varest

Logical; if TRUE the estimate' variances and standard errors are returned. FALSE is the default.

taper

String; the name of the taper correlation function.

type

String; the type of the likelihood objects. If Pairwise (the default) then the marginal composite likelihood is formed by pairwise marginal likelihoods.

upper

An optional named list giving the values for the upper bound of the space parameter when the optimizer is or L-BFGS-B or nlminb or optimize. The names of the list must be the same of the names in the start list.

X

Numeric; Matrix of spatio(temporal)covariates in the linear mean specification.

neighb

Numeric;parameter for vecchia approximation using GPvecchia package

MM

Numeric;a non constant fixed mean

aniso

Logical; should anisotropy be considered?

Value

Return a list from an optim call.

Author(s)

Moreno Bevilacqua, [e-mail],https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, [e-mail], https://sites.google.com/site/moralesonatevictor/, Christian", Caamaño-Carrillo, [e-mail],https://www.researchgate.net/profile/Christian-Caamano

See Also

GeoFit