Covariogram {CompRandFld} | R Documentation |
The procedure computes and/or plots the covariance, the variogram or the extremal coefficient functions and the practical range estimated fitting a Gaussian or max-stable random field with the composite-likelihood or using the weighted least square method. Allows to add to the variogram or extremal coefficient plots the empirical estimates.
Covariogram(fitted, lags=NULL, lagt=NULL, answer.cov=FALSE, answer.vario=FALSE, answer.extc=FALSE, answer.range=FALSE, fix.lags=NULL, fix.lagt=NULL, show.cov=FALSE, show.vario=FALSE, show.extc=FALSE, show.range=FALSE, add.cov=FALSE, add.vario=FALSE, add.extc=FALSE, pract.range=95, vario, ...)
fitted |
A fitted object obtained from the
|
lags |
A numeric vector of distances. |
lagt |
A numeric vector of temporal separations. |
answer.cov |
Logical; if |
answer.vario |
Logical; if |
answer.extc |
Logical; if |
answer.range |
Logical; if |
fix.lags |
Integer; a positive value denoting the spatial lag to consider for the plot of the temporal profile. |
fix.lagt |
Integer; a positive value denoting the temporal lag to consider for the plot of the spatial profile. |
show.cov |
Logical; if |
show.vario |
Logical; if |
show.extc |
Logical; if |
show.range |
Logical; if |
add.cov |
Logical; if |
add.vario |
Logical; if |
add.extc |
Logical; if |
pract.range |
Numeric; the percent of the sill to be reached. |
vario |
A |
... |
other optional parameters which are passed to plot functions. |
The returned object is eventually a list with:
covariance |
The vector of the estimated covariance function; |
variogram |
The vector of the estimated variogram function; |
extrcoeff |
The vector of the estimated extremal coefficient function; |
pratical.range |
The estimated practial range. |
Simone Padoan, simone.padoan@unibocconi.it, http://faculty.unibocconi.it/simonepadoan; Moreno Bevilacqua, moreno.bevilacqua@uv.cl, https://sites.google.com/a/uv.cl/moreno-bevilacqua/home.
Padoan, S. A. and Bevilacqua, M. (2015). Analysis of Random Fields Using CompRandFld. Journal of Statistical Software, 63(9), 1–27.
Cooley, D., Naveau, P. and Poncet, P. (2006) Variograms for spatial max-stable random fields. Dependence in Probability and Statistics, p. 373–390.
Cressie, N. A. C. (1993) Statistics for Spatial Data. New York: Wiley.
Gaetan, C. and Guyon, X. (2010) Spatial Statistics and Modelling. Spring Verlang, New York.
Smith, R. L. (1990) Max-Stable Processes and Spatial Extremes. Unpublished manuscript, University of North California.
library(CompRandFld) library(RandomFields) library(scatterplot3d) set.seed(31231) # Set the coordinates of the points: x <- runif(100, 0, 10) y <- runif(100, 0, 10) coords<-cbind(x,y) ################################################################ ### ### Example 1. Plot of covariance and variogram functions ### estimated from a Gaussian random field with exponent ### correlation. One spatial replication is simulated. ### ### ############################################################### # Set the model's parameters: corrmodel <- "exponential" mean <- 0 sill <- 1 nugget <- 0 scale <- 2 # Simulation of the Gaussian random field: data <- RFsim(coordx=coords, corrmodel=corrmodel, param=list(mean=mean, sill=sill, nugget=nugget, scale=scale))$data # Maximum composite-likelihood fitting of the Gaussian random field: start<-list(scale=scale,sill=sill,mean=mean(data)) fixed<-list(nugget=nugget) # Maximum composite-likelihood fitting of the random field: fit <- FitComposite(data, coordx=coords, corrmodel=corrmodel,likelihood="Marginal", type="Pairwise",start=start,fixed=fixed,maxdist=6) # Results: print(fit) # Empirical estimation of the variogram: vario <- EVariogram(data, x, y) # Plot of covariance and variogram functions: par(mfrow=c(1,2)) Covariogram(fit, show.cov=TRUE, show.range=TRUE, show.vario=TRUE, vario=vario,pch=20) ################################################################ ## ### Example 2. Plot of covariance and extremal coefficient ### functions estimated from a max-stable random field with ### exponential correlation. n idd spatial replications are ### simulated. ### ############################################################### set.seed(1156) # Simulation of the max-stable random field: data <- RFsim(coordx=coords, corrmodel=corrmodel, model="ExtGauss", replicates=20, param=list(mean=mean,sill=sill,nugget=nugget,scale=scale))$data start=list(sill=sill,scale=scale) # Maximum composite-likelihood fitting of the max-stable random field: fit <- FitComposite(data, coordx=coords, corrmodel=corrmodel, model='ExtGauss', replicates=20, varest=TRUE, vartype='Sampling', margins="Frechet",start=start) data <- Dist2Dist(data, to='sGumbel') # Empirical estimation of the madogram: vario <- EVariogram(data, coordx=coords, type='madogram', replicates=20) # Plot of correlation and extremal coefficient functions: par(mfrow=c(1,2)) Covariogram(fit, show.cov=TRUE, show.range=TRUE, show.extc=TRUE, vario=vario, pract.range=84,pch=20) ################################################################ ### ### Example 3. Plot of covariance and variogram functions ### estimated from a Gaussian spatio-temporal random field with ### double-exp correlation. ### One spatio-temporal replication is simulated. ### ############################################################### # Define the spatial-coordinates of the points: #x <- runif(20, 0, 1) #y <- runif(20, 0, 1) # Define the temporal sequence: #time <- seq(0, 30, 1) # Simulation of the spatio-temporal Gaussian random field: #data <- RFsim(x, y, time, corrmodel="exp_exp",param=list(mean=mean, # nugget=nugget,scale_s=0.5,scale_t=1,sill=sill))$data # Maximum composite-likelihood fitting of the space-time Gaussian random field: #fit <- FitComposite(data, x, y, time, corrmodel="exp_exp", maxtime=5, # likelihood="Marginal",type="Pairwise", fixed=list( # nugget=nugget, mean=mean),start=list(scale_s=0.2, # scale_t=1, sill=sill)) # Empirical estimation of spatio-temporal covariance: #vario <- EVariogram(data, x, y, time, maxtime=10) # Plot of the fitted space-time covariace #Covariogram(fit,show.cov=TRUE) # Plot of the fitted space-time variogram #Covariogram(fit,vario=vario,show.vario=TRUE) # Plot of covariance, variogram and spatio and temporal profiles: #Covariogram(fit,vario=vario,fix.lagt=1,fix.lags=1,show.vario=TRUE,pch=20) ################################################################ ### ### Example 4. Plot of parametric and empirical lorelograms ### estimated from a Binary Gaussian random fields with ### exponential correlation. One spatial replication is ### simulated. ### ############################################################### #set.seed(1240) # Define the spatial-coordinates of the points: #x <- seq(0,3, 0.1) #y <- seq(0,3, 0.1) # Simulation of the Binary Gaussian random field: #data <- RFsim(x, y, corrmodel=corrmodel, model="BinaryGauss", # threshold=0,param=list(nugget=nugget,mean=mean, # scale=.6,sill=0.8))$data # Maximum composite-likelihood fitting of the Binary Gaussian random field: #fit <- FitComposite(data, x, y, corrmodel=corrmodel, model="BinaryGauss", # maxdist=0.8, likelihood="Marginal", type="Pairwise", # start=list(mean=mean,scale=0.1,sill=0.1)) # Empirical estimation of the lorelogram: #vario <- EVariogram(data, x, y, type="lorelogram", maxdist=2) # Plot of fitted and empirical lorelograms: #Covariogram(fit, vario=vario, show.vario=TRUE, lags=seq(0.1,2,0.1),pch=20)