GeoNeighborhood {GeoModels}

Spatio (temporal) neighborhood selection for local kriging.

Description

Given a set of spatio (temporal) locations and data, the procedure selects a spatio (temporal) neighborhood associated to some given spatio (temporal) locations. The neighborhood is computed using a fixed spatio (temporal) threshold or considering a fixed number of spatio (temporal) neighbors.

Usage

GeoNeighborhood(data=NULL, coordx, coordy=NULL,
coordt=NULL, coordx_dyn=NULL, bivariate=FALSE,
               distance="Eucl", grid=FALSE, 
               loc, neighb=NULL,maxdist=NULL,
               maxtime=NULL, radius=6371, time=NULL, 
               X=NULL,M=NULL,spobj=NULL,spdata=NULL)

Arguments

data

An optional d-dimensional vector (a single spatial realisation) or a (d \times d)-matrix (a single spatial realisation on regular grid) or a (t \times d)-matrix (a single spatial-temporal realisation) or an (d \times d \times t \times n )-array (a single spatial-temporal realisation on regular grid).

coordx

A numeric (d \times 2)-matrix (where d is the number of spatial sites) giving 2-dimensions of spatial coordinates or a numeric d-dimensional vector giving 1-dimension of spatial coordinates. 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; 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 giving 1-dimension of temporal coordinates. Optional argument, the default is NULL then a spatial RF 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

bivariate

If TRUE then data is considered as spatial bivariate data.

distance

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

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).

loc

A (1 \times 2)-matrix giving the spatial coordinate of the location for which a neighborhood is computed .

neighb

Numeric; an optional positive integer indicating the order of spatial neighborhood.

maxdist

Numeric; a positive value indicating the maximum spatial distance considered in the spatial neighborhood selection.

maxtime

Numeric; an optional positive integer indicating the order of temporal neighborhood.

radius

Numeric; a value indicating the radius of the sphere when using the great circle distance. Default value is the radius of the earth in Km (i.e. 6371)

time

Numeric; a value giving the temporal instant for which a neighborhood is computed.

X

Numeric; an optional Matrix of spatio (temporal) covariates.

M

Numeric; an estimated spatio (temporal) mean vector.

spobj

An object of class sp or spacetime

spdata

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

Value

Returns a list containing the following informations:

coordx

A list of the matrix coordinates of the computed spatial neighborhood ;

coordt

A vector of the computed temporal neighborhood;

data

A list of the vector of data associated with the spatio (temporal) neighborhood;

distance

The type of spatial distance;

numcoord

The vector of numbers of location sites involved the spatial neighborhood;

numtime

The vector of numbers of temporal insttants involved the temporal neighborhood;

radius

The radius of the sphere if coordinates are passed in lon/lat format;

spacetime

TRUE if spatio-temporal and FALSE if spatial RF;

X

The matrix of spatio (temporal) covariates associated with the computed spatio (temporal) neighborhood;

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

Examples

library(GeoModels)
##########################################
#### Example: spatial neighborhood  ######
##########################################
set.seed(75)
coords=cbind(runif(500),runif(500))

param=list(nugget=0,mean=0,scale=0.2,sill=1,
            power2=4,smooth=1)

data_all = GeoSim(coordx=coords, corrmodel="GenWend", 
                         param=param)$data

plot(coords)
##two locations 
loc_to_pred=matrix(c(0.3,0.5,0.7,0.2),2,2)

points(loc_to_pred,pch=20)
neigh=GeoNeighborhood(data_all, coordx=coords,  
                  loc=loc_to_pred,neighb=8)

# two Neighborhoods 
neigh$coordx
points(neigh$coordx[[1]],pch=20,col="red")
points(neigh$coordx[[2]],pch=20,col="blue")
# associated data
neigh$data


###################################################
#### Example: spatio temporal spatial neighborhood#  
###################################################

set.seed(78)
coords=matrix(runif(80),40,2)
coordt=seq(0,6,0.25)

param=list(nugget=0,mean=0,scale_s=0.2/3,scale_t=0.25/3,sill=2)

data_all = GeoSim(coordx=coords, coordt=coordt,corrmodel="Exp_Exp", 
                         param=param)$data
##  two location to predict
loc_to_pred=matrix(runif(4),2,2)
## three temporal instants to predict
time=c(1,2)

plot(coords,xlim=c(0,1),ylim=c(0,1))
points(loc_to_pred,pch=20)

neigh=GeoNeighborhood(data_all, coordx=coords,  coordt=coordt,
                  loc=loc_to_pred,time=time,neighb=3,maxtime=0.5)

# first spatio-temporal neighborhoods 
# with  associated data
neigh$coordx[[1]]
neigh$coordt[[1]]
neigh$data[[1]]

###################################################
#### Example: bivariate  spatial neighborhood #####  
###################################################

set.seed(79)
coords=matrix(runif(100),50,2)

param=list(mean_1=0,mean_2=0,scale=0.12,smooth=0.5,
           sill_1=1,sill_2=1,nugget_1=0,nugget_2=0,pcol=0.5)

data_all = GeoSim(coordx=coords,corrmodel="Bi_matern_sep",
                 param=param)$data
##  two location to predict
loc_to_pred=matrix(runif(4),2,2)

neigh=GeoNeighborhood(data_all, coordx=coords,bivariate=TRUE,
                  loc=loc_to_pred,maxdist=0.25)

plot(coords)
points(loc_to_pred,pch=20)
points(neigh$coordx[[1]],col="red",pch=20)
points(neigh$coordx[[2]],col="red",pch=20)