Max-Likelihood-Based Fitting of Gaussian and non Gaussian RFs.
Maximum weighted composite-likelihood fitting for Gaussian and some Non-Gaussian univariate spatial, spatio-temporal and bivariate spatial RFs. A first preliminary estimation is performed using independence composite-likelihood for the marginal parameters of the model. The estimates are then used as starting values in the second final estimation step. The function allows to fix any of the parameters and setting upper/lower bound in the optimization. UTF-8
GeoFit2(data, coordx, coordy=NULL, coordz=NULL,coordt=NULL, coordx_dyn=NULL, copula=NULL,corrmodel,distance="Eucl",fixed=NULL, anisopars=NULL,est.aniso=c(FALSE,FALSE),GPU=NULL, grid=FALSE, likelihood='Marginal', local=c(1,1), lower=NULL,maxdist=Inf,neighb=NULL, maxtime=Inf, memdist=TRUE,method="cholesky", model='Gaussian',n=1, onlyvar=FALSE , optimizer='Nelder-Mead', parallel=FALSE, radius=6371, sensitivity=FALSE,sparse=FALSE, start=NULL, taper=NULL, tapsep=NULL, type='Pairwise', upper=NULL, varest=FALSE, weighted=FALSE,X=NULL,nosym=FALSE,spobj=NULL,spdata=NULL)
data: A -dimensional vector (a single spatial realisation) or a ()-matrix (a single spatial realisation on regular grid) or a ()-matrix (a single spatial-temporal realisation) or an ()-array (a single spatial-temporal realisation on regular grid). For the description see the Section Details .
coordx: A numeric ()-matrix or ()-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 RF is expected.
coordx_dyn: A list of numeric ()-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.
GPU: Numeric; if NULL (the default) no OpenCL computation is performed. The user can choose the device to be used. Use DeviceInfo() function to see available devices, only double precision devices are allowed
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 the Section Details .
local: Numeric; number of local work-items of the OpenCL setup
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.
maxdist: Numeric; an optional positive value indicating the maximum spatial distance considered in the composite or tapered likelihood computation. See the Section Details for more information.
neighb: Numeric; an optional positive integer indicating the order of neighborhood in the composite likelihood computation. See the Section Details for more information.
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.
method: String; the type of matrix decomposition used in the simulation. Default is cholesky. The other possible choices is svd.
model: String; the type of RF and therefore the densities associated to the likelihood objects. Gaussian is the default, see the Section Details .
n: Numeric; number of trials in a binomial RF; number of successes in a negative binomial RF
onlyvar: Logical; if TRUE (and varest is TRUE) only the variance covariance matrix is computed without optimizing. FALSE is the default.
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 optmization is performed using optimParallel using the maximum number of cores, when optimizer is L-BFGS-B.FALSE is the default.
radius: Numeric; the radius of the sphere in the case of lon-lat coordinates. The default is 6371, the radius of the earth.
sensitivity: Logical; if TRUE then the sensitivy matrix is computed
sparse: Logical; if TRUE then maximum likelihood is computed using sparse matrices algorithms (spam packake).It should be used with compactly supported covariance models.FALSE is the default.
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 Details ).
taper: String; the name of the type of covariance matrix. It can be Standard (the default value) or Tapering for taperd covariance matrix.
tapsep: Numeric; an optional value indicating the separabe parameter in the space time adaptive taper (see Details ).
type: String; the type of the likelihood objects. If Pairwise (the default) then the marginal composite likelihood is formed by pairwise marginal likelihoods (see Details ).
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 bobyqa or optimize. The names of the list must be the same of the names in the start list.
varest: Logical; if TRUE the estimates' variances and standard errors are returned. For composite likelihood estimation it is deprecated. Use sensitivity TRUE and update the object using the function GeoVarestbootstrap
FALSE is the default.
weighted: Logical; if TRUE the likelihood objects are weighted, see the Section Details . 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
The function GeoFit2 is similar to the function GeoFit. However GeoFit2 performs a preliminary estimation using maximum indenpendence composite likelihood of the marginal parameters of the model and then use the obtained estimates as starting value in the global weighted composite likelihood estimation (that includes marginal and dependence parameters). This allows to obtain "good" starting values in the optimization algorithm for the marginal parameters.
Returns an object of class GeoFit. An object of class GeoFit is a list containing at most the following components: - bivariate: Logical:TRUE if the Gaussian RF is bivariate, otherwise FALSE;
clic: The composite information criterion, if the full likelihood is considered then it coincides with the Akaike information criterion;
coordx: A -dimensional vector of spatial coordinates;
coordy: A -dimensional vector of spatial coordinates;
coordt: A -dimensional vector of temporal coordinates;
coordx_dyn: A list of dynamical (in time) spatial coordinates;
conf.int: Confidence intervals for standard maximum likelihood estimation;
convergence: A string that denotes if convergence is reached;
copula: The type of copula;
corrmodel: The correlation model;
data: The vector or matrix or array of data;
distance: The type of spatial distance;
fixed: A list of the fixed parameters;
iterations: The number of iteration used by the numerical routine;
likelihood: The configuration of the composite likelihood;
logCompLik: The value of the log composite-likelihood at the maximum;
maxdist: The maximum spatial distance used in the weigthed composite likelihood. If no spatial distance is specified then it is NULL;
maxtime: The maximum temporal distance used in the weigthed composite likelihood. If no spatial distance is specified then it is NULL;
message: Extra message passed from the numerical routines;
model: The density associated to the likelihood objects;
missp: True if a misspecified Gaussian model is ued in the composite likelihhod;
n: The number of trials in a binominal RF;the number of successes in a negative Binomial RFs;
neighb: The order of spatial neighborhood in the composite likelihood computation.
ns: The number of (different) location sites in the bivariate case;
nozero: In the case of tapered likelihood the percentage of non zero values in the covariance matrix. Otherwise is NULL.
numcoord: The number of spatial coordinates;
numtime: The number of the temporal realisations of the RF;
param: A list of the parameters' estimates;
radius: The radius of the sphere in the case of great circle distance;
stderr: The vector of standard errors for standard maximum likelihood estimation;
sensmat: The sensitivity matrix;
varcov: The matrix of the variance-covariance of the estimates;
type: The type of the likelihood objects.
X: The matrix of covariates;
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
library(GeoModels) ############################################################### ############ Examples of spatial Gaussian RFs ################ ############################################################### ################################################################ ### ### Example 1 : Maximum pairwise conditional likelihood fitting ### of a Gaussian RF with Matern correlation ### ############################################################### model="Gaussian" # Define the spatial-coordinates of the points: set.seed(3) N=400 # number of location sites x <- runif(N, 0, 1) set.seed(6) y <- runif(N, 0, 1) coords <- cbind(x,y) # Define spatial matrix covariates X=cbind(rep(1,N),runif(N)) # Set the covariance model's parameters: corrmodel <- "Matern" mean <- 0.2 mean1 <- -0.5 sill <- 1 nugget <- 0 scale <- 0.2/3 smooth=0.5 param<-list(mean=mean,mean1=mean1,sill=sill,nugget=nugget,scale=scale,smooth=smooth) # Simulation of the spatial Gaussian RF: data <- GeoSim(coordx=coords,model=model,corrmodel=corrmodel, param=param,X=X)$data fixed<-list(nugget=nugget,smooth=smooth) start<-list(mean=mean,mean1=mean1,scale=scale,sill=sill) ################################################################ ### ### Maximum pairwise likelihood fitting of ### Gaussian RFs with exponential correlation. ### ############################################################### fit1 <- GeoFit2(data=data,coordx=coords,corrmodel=corrmodel, optimizer="BFGS",neighb=3,likelihood="Conditional", type="Pairwise", start=start,fixed=fixed,X=X) print(fit1) ############################################################### ############ Examples of spatial non-Gaussian RFs ############# ############################################################### ################################################################ ### ### Example 2. Maximum pairwise likelihood fitting of ### a LogGaussian RF with Generalized Wendland correlation ### ############################################################### set.seed(524) # Define the spatial-coordinates of the points: N=500 x <- runif(N, 0, 1) y <- runif(N, 0, 1) coords <- cbind(x,y) X=cbind(rep(1,N),runif(N)) mean=1; mean1=2 # regression parameters nugget=0 sill=0.5 scale=0.2 smooth=0 model="LogGaussian" corrmodel="GenWend" param=list(mean=mean,mean1=mean1,sill=sill,scale=scale, nugget=nugget,power2=4,smooth=smooth) # Simulation of a non stationary LogGaussian RF: data <- GeoSim(coordx=coords, corrmodel=corrmodel,model=model,X=X, param=param)$data fixed<-list(nugget=nugget,power2=4,smooth=smooth) start<-list(mean=mean,mean1=mean1,scale=scale,sill=sill) I=Inf lower<-list(mean=-I,mean1=-I,scale=0,sill=0) upper<-list(mean= I,mean1= I,scale=I,sill=I) # Maximum pairwise composite-likelihood fitting of the RF: fit <- GeoFit2(data=data,coordx=coords,corrmodel=corrmodel, model=model, neighb=3,likelihood="Conditional",type="Pairwise",X=X, optimizer="nlminb",lower=lower,upper=upper, start=start,fixed=fixed) print(unlist(fit$param)) ################################################################ ### ### Example 3. Maximum pairwise likelihood fitting of ### SinhAsinh RFs with Wendland0 correlation ### ############################################################### set.seed(261) model="SinhAsinh" # Define the spatial-coordinates of the points: x <- runif(500, 0, 1) y <- runif(500, 0, 1) coords <- cbind(x,y) corrmodel="Wend0" mean=0;nugget=0 sill=1 skew=-0.5 tail=1.5 power2=4 c_supp=0.2 # model parameters param=list(power2=power2,skew=skew,tail=tail, mean=mean,sill=sill,scale=c_supp,nugget=nugget) data <- GeoSim(coordx=coords, corrmodel=corrmodel,model=model, param=param)$data plot(density(data)) fixed=list(power2=power2,nugget=nugget) start=list(scale=c_supp,skew=skew,tail=tail,mean=mean,sill=sill) # Maximum pairwise likelihood: fit1 <- GeoFit2(data=data,coordx=coords,corrmodel=corrmodel, model=model, neighb=3,likelihood="Marginal",type="Pairwise", start=start,fixed=fixed) print(unlist(fit1$param))