GeoNeighbSelect function

A brute force algorithm for spatial or spatiotemoral optimal neighboord selection for pairwise composite likelihood estimation.

The procedure performs different pairwise composite likelihood estimation using user's specified spatial or spatiotemporal neighboords in the weight function. The neighbor minimizing the sum of the squared differences between the estimated semivariogram and the empirical semivariogram is selected. The procedure needs an object obtained using the GeoVariogram function. UTF-8

GeoNeighbSelect(data, coordx, coordy=NULL,coordz=NULL, coordt=NULL, coordx_dyn=NULL,
    copula=NULL,corrmodel=NULL, distance="Eucl",fixed=NULL,anisopars=NULL,
    est.aniso=c(FALSE,FALSE), grid=FALSE, likelihood='Marginal',lower=NULL,
    neighb=c(1,2,3,4,5),maxtime=Inf, memdist=TRUE,model='Gaussian',
    n=1, ncores=NULL,optimizer='Nelder-Mead', parallel=FALSE, 
    bivariate=FALSE,radius=6371, start=NULL,type='Pairwise', upper=NULL, 
    weighted=FALSE,X=NULL,nosym=FALSE,spobj=NULL,spdata=NULL,vario=NULL)

Arguments

• data: A $d$-dimensional vector (a single spatial realisation) or a ($d x d$)-matrix (a single spatial realisation on regular grid) or a ($t x d$)-matrix (a single spatial-temporal realisation) or an ($d x d x t$)-array (a single spatial-temporal realisation on regular grid). For the description see the Section Details .

• coordx: A numeric ($d x 2$)-matrix or ($d x 3$)-matrix Coordinates on a sphere for a fixed radius radius

  are passed in lon/lat format expressed in decimal degrees.

• coordy: A numeric vector giving 1-dimension of spatial coordinates; Optional argument, the default is NULL.

• coordz: A numeric vector giving 1-dimension of spatial coordinates; Optional argument, the default is NULL.

• coordt: A numeric vector assigning 1-dimension of temporal coordinates. Optional argument, the default is NULL

  then a spatial random fields is expected.

• coordx_dyn: A list of $m$ numeric ($d x 2$)-matrices containing dynamical (in time) spatial coordinates. Optional argument, the default is NULL

• copula: String; the type of copula. It can be "Clayton" or "Gaussian"

• corrmodel: String; the name of a correlation model, for the description see the Section Details .

• distance: String; the name of the spatial distance. The default is Eucl, the euclidean distance. See the Section Details .

• fixed: An optional named list giving the values of the parameters that will be considered as known values. The listed parameters for a given correlation function will be not estimated.

• anisopars: A list of two elements: "angle" and "ratio" i.e. the anisotropy angle and the anisotropy ratio, respectively.

• est.aniso: A bivariate logical vector providing which anisotropic parameters must be estimated.

• grid: Logical; if FALSE (the default) the data are interpreted as spatial or spatial-temporal realisations on a set of non-equispaced spatial sites (irregular grid).

• likelihood: String; the configuration of the composite likelihood. Marginal is the default (see Section Details in GeoFit ).

• 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 bobyqa or optimize. The names of the list must be the same of the names in the start list.

• neighb: Numeric; a vector of positive integers indicating the order of neighborhood in the weight function of composite likelihood (see Section Details in GeoFit ).

• maxtime: Numeric; an optional positive integer indicating the order of temporal neighborhood in the composite likelihood computation.

• memdist: Logical; if TRUE then all the distances useful in the composite likelihood estimation are computed before the optimization. FALSE is deprecated.

• model: String; the type of random fields and therefore the densities associated to the likelihood objects. Gaussian is the default, see the Section Details in GeoFit .

• n: Numeric; number of trials in a binomial random fields; number of successes in a negative binomial random fields

• ncores: Numeric; the number of cores involved in the parallelization

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

• parallel: Logical; if TRUE the procedure is parallelized using dofuture.

• bivariate: Logical; if TRUE the bivariate case is considered.

• radius: Numeric; the radius of the sphere in the case of lon-lat coordinates. The default is 6371, the radius of the earth.

• start: An optional named list with the initial values of the parameters that are used by the numerical routines in maximization procedure. NULL is the default (see Section Details in GeoFit ).

• type: String; the type of the likelihood objects. If Pairwise (the default) then the marginal composite likelihood is formed by pairwise marginal likelihoods (see Section Details in GeoFit ).

• 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 bobyqa or nlminb or optimize. The names of the list must be the same of the names in the start list.

• weighted: Logical; if TRUE the likelihood objects are weighted (see Section Details in GeoFit ). If FALSE (the default) the composite likelihood is not weighted.

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

• nosym: Logical; if TRUE simmetric weights are not considered. This allows a faster but less efficient CL estimation.

• spobj: An object of class sp or spacetime

• spdata: Character:The name of data in the sp or spacetime object

• vario: An object of the class GeoVariogram obtained using the GeoVariogram function

Details

The procedure performs different pairwise composite likelihood estimation using user's specified spatial or spatiotemporal neighboords in the weight function. The neighbor minimizing the sum of the squared differences between the estimated semivariogram and the empirical semivariogram is selected. The procedure needs an object obtained using the GeoVariogram function.

Returns

Returns a list with information on the best selected neighbor.

Author(s)

Moreno Bevilacqua, moreno.bevilacqua89@gmail.com ,https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, victor.morales@uv.cl , https://sites.google.com/site/moralesonatevictor/, Christian", Caamaño-Carrillo, chcaaman@ubiobio.cl ,https://www.researchgate.net/profile/Christian-Caamano

Examples

library(GeoModels)

######### spatial case
set.seed(32)
N=500  # number of location sites
x <- runif(N, 0, 1)
y <- runif(N, 0, 1)
coords <- cbind(x,y)
mean <- 0.2
# Set the covariance model's parameters:
corrmodel <- "Matern"
sill <- 1;nugget <- 0
scale <- 0.2/3;smooth=0.5

model="Gaussian"
param<-list(mean=mean,sill=sill,nugget=nugget,scale=scale,smooth=smooth)
# Simulation 
data <- GeoSim(coordx=coords,corrmodel=corrmodel, param=param,model=model)$data
I=Inf
fixed<-list(nugget=nugget)
start<-list(mean=mean,scale=scale,smooth=smooth,sill=sill)
lower<-list(mean=-I,scale=0,sill=0,smooth=0)
upper<-list(mean=I,scale=I,sill=I,smooth=I)

vario = GeoVariogram(coordx=coords,data=data,maxdist=0.3,numbins=15)

neighb=c(1,2,3,4) ## trying  different neighbs
selK <- GeoNeighbSelect(vario=vario,data=data,coordx=coords,corrmodel=corrmodel, 
                        model=model,neighb=neighb,
                        likelihood="Conditional",type="Pairwise",parallel=FALSE,
                        optimizer="nlminb",lower=lower,upper=upper,
                        start=start,fixed=fixed)
print(selK$best_neighb) ## selected neighbor