GeoResiduals: Compute Residuals from a Fitted GeoModels Model

In GeoModels: Procedures for Gaussian and Non Gaussian Geostatistical (Large) Data Analysis

Compute Residuals from a Fitted GeoModels Model

Description

The procedure return a GeoFit object associated to the estimated residuals. For a random field Y defined on the real line (Gaussian, Skew Gaussian, Tukeyh etcc) they are computed as (Y-m)/sqrt(v) where m and v are the estimated mean and variance respectively. For a random field Y defined on the positive real line (Gamma, Weibull, Log-Gaussian) they are computed as Y/m where m is the estimated mean. In the first case residuals have zero mean and unut variance with a specific distribution defined on the real line. In the second case residuals have unit mean with a specific distribution defined on the positive real line. For the discrete Bernoulli/Binary, Binomial, Geometric/negative-binomial, Poisson, and Poisson–Gamma models, the function returns Pearson residuals computed from the fitted marginal mean and variance. The paper specifies these marginal moments but does not prescribe a residual definition; Pearson residuals are an explicit package convention. For continuous models, the returned object can be coupled with GeoQQ and GeoCovariogram. For discrete Pearson residuals, use the returned object for residual maps and variograms, and apply GeoQQ() or GeoPit() to the original fitted object for marginal assessment.

Usage

GeoResiduals(fit)

Arguments

fit	A fitted object obtained from the GeoFit.

Details

The fitted location is evaluated from the full mean specification: a site-specific fixed mean vector when present, otherwise X\beta with coefficients mean, mean1, and so on matched in order to the columns of X. The returned residual object is converted to an intercept-only, standardized representation for subsequent diagnostics. All other fields of the original GeoFit object, including neighbourhood, thinning, anisotropy, convergence, and pair-selection metadata, are preserved.

For Beta2 and Kumaraswamy2, the residual transformation uses the fitted support min/max and the corresponding fitted marginal CDF, so the standardized residual scale is the unit interval.

For the discrete models described in the package paper, Pearson residuals are used: (Y-E(Y))/\sqrt{Var(Y)}. Thus p=\Phi(\mu) for Bernoulli, Binomial and negative-binomial fields, while \lambda=\exp(\mu) for Poisson fields. For Poisson–Gamma fields, with fitted mean \lambda and shape \kappa, the fitted variance is \lambda(1+\lambda/\kappa). These deterministic residuals are intended for residual maps and variograms; they are not randomized quantile residuals, and GeoQQ() intentionally rejects the Pearson-residual object. Bivariate residuals are currently supported only for Gaussian models.

Value

Returns an (updated) object of class GeoFit. The component residual_type records whether the data are Pearson or model-standardized residuals.

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.

Examples

library(GeoModels)



###########################
###Example 1: Residuals using a Gaussian RF
###########################
set.seed(211)
model="Gaussian";
N=700 # number of location sites
# Set the coordinates of the points:
x = runif(N, 0, 1)
y = runif(N, 0, 1)
coords=cbind(x,y)

# regression parameters
mean = 5
mean1=0.8

X=cbind(rep(1,N),runif(N))
# correlation parameters:
corrmodel = "Wend0"
sill = 1
nugget = 0
scale = 0.3
power2=4

param=list(mean=mean,mean1=mean1, sill=sill, nugget=nugget, 
 scale=scale,power2=power2)
# Simulation of the Gaussian RF:
data = GeoSim(coordx=coords, corrmodel=corrmodel, X=X,model=model,param=param)$data

start=list(mean=mean,mean1=mean1, scale=scale,sill=sill)
fixed=list(nugget=nugget,power2=power2)
# Maximum composite-likelihood fitting 
fit = GeoFit(data,coordx=coords, corrmodel=corrmodel,model=model,X=X,
 likelihood="Conditional",type='Pairwise',start=start,
 fixed=fixed,neighb=3)

res=GeoResiduals(fit)
mean(res$data) # should be approx 0
var(res$data) # should be approx 1
# checking goodness of fit marginal model
GeoQQ(res);GeoQQ(res,type="D",col="red",ylim=c(0,0.5),breaks=20);
# Empirical estimation of the variogram for the residuals:
vario = GeoVariogram(res$data,coordx=coords,maxdist=0.5)
# Comparison between empirical amd estimated semivariogram for the residuals
GeoCovariogram(res, show.vario=TRUE, vario=vario,pch=20)





###########################
###Example 2: Residuals using a Weibull RF
###########################
model="Weibull";shape=4
N=700 # number of location sites
# Set the coordinates of the points:
x = runif(N, 0, 1)
y = runif(N, 0, 1)
coords=cbind(x,y)


# regression parameters
mean = 5
mean1=0.8

X=cbind(rep(1,N),runif(N))
# correlation parameters:
corrmodel = "Wend0"
sill = 1
nugget = 0
scale = 0.3
power2=4

param=list(mean=mean,mean1=mean1, sill=sill, nugget=nugget, 
	 scale=scale,shape=shape,power2=power2)
# Simulation of the Gaussian RF:
data = GeoSim(coordx=coords, corrmodel=corrmodel, X=X,model=model,param=param)$data

I=Inf
start=list(mean=mean,mean1=mean1, scale=scale,shape=shape)
lower=list(mean=-I,mean1=-I, scale=0,shape=0)
upper=list(mean= I,mean1= I, scale=I,shape=I)
fixed=list(nugget=nugget,sill=sill,power2=power2)
# Maximum composite-likelihood fitting 
fit = GeoFit(data,coordx=coords, corrmodel=corrmodel,model=model,X=X,
 likelihood="Conditional",type='Pairwise',start=start,
 optimizer="nlminb", lower=lower,upper=upper,
 fixed=fixed,neighb=3)


res=GeoResiduals(fit)
mean(res$data) # should be approx 1
# checking goodness of fit marginal model
GeoQQ(res);GeoQQ(res,type="D",lwd=2,ylim=c(0,1.7),breaks=20);
# Empirical estimation of the variogram for the residuals:
vario = GeoVariogram(res$data,coordx=coords,maxdist=0.5)
# Comparison between empirical amd estimated semivariogram for the residuals
GeoCovariogram(res, show.vario=TRUE, vario=vario,pch=20)

GeoModels documentation built on Sept. 23, 2026, 5:07 p.m.