georobModelBuilding: S3 Methods for Stepwise Building Fixed-Effects Models for...
In georob: Robust Geostatistical Analysis of Spatial Data
georobModelBuilding R Documentation
S3 Methods for Stepwise Building Fixed-Effects Models for Class georob
Description
This page documents the methods deviance,
logLik, extractAIC, add1, drop1,
step and waldtest for the class georob. The package
georob provides a generic step function and a default
method which is identical with the (non-generic) function
step.
Usage
## S3 method for class 'georob'
deviance(object, warn = TRUE, REML = FALSE, ...)
## S3 method for class 'georob'
logLik(object, warn = TRUE, REML = FALSE, ...)
## S3 method for class 'georob'
extractAIC(fit, scale = 0, k = 2, ...)
## S3 method for class 'georob'
add1(object, scope, scale = 0, test = c("none", "Chisq"), k = 2,
trace = FALSE, fixed = TRUE, use.fitted.param = TRUE, verbose = 0,
ncores = 1, ...)
## S3 method for class 'georob'
drop1(object, scope, scale = 0, test = c("none", "Chisq"), k = 2,
trace = FALSE, fixed = TRUE, use.fitted.param = TRUE, verbose = 0,
ncores = 1, ...)
step(object, ...)
## Default S3 method:
step(object, scope, scale = 0,
direction = c("both", "backward", "forward"), trace = 1,
keep = NULL, steps = 1000, k = 2, ...)
## S3 method for class 'georob'
step(object, scope, scale = 0,
direction = c("both", "backward", "forward"), trace = 1,
keep = NULL, steps = 1000, k = 2,
fixed.add1.drop1 = TRUE, fixed.step = fixed.add1.drop1,
use.fitted.param = TRUE, verbose = 0, ncores = 1, ...)
## S3 method for class 'georob'
waldtest(object, ..., vcov = NULL, test = c("F", "Chisq"),
name = NULL)
Arguments
object, fit
an object of class georob, see
georobObject.
direction
a character keyword with the mode of stepwise search,
see step.
fixed, fixed.add1.drop1
a logical scalar controlling whether the
variogram parameters are not adjusted when adding or
dropping model terms by add1 and drop1 (default
TRUE), see Details.
fixed.step
a logical scalar controlling whether the variogram
parameters are not adjusted after having called add1 and
drop1 in step (default TRUE), see Details.
k
a numeric specifying the 'weight' of the equivalent degrees of
freedom (=: edf) part in the AIC formula, see
extractAIC.
keep
a filter function whose input is a fitted model object and the
associated AIC statistic, and whose output is arbitrary,
see step.
name
a function for extracting a suitable name/description from a
fitted model object. By default the name is queried by calling
formula, see
waldtest.
ncores
an integer specifying the number of cores used for
parallelized execution of add1 and drop1. If larger than
one then the minimum of ncores, parallel::detectCores()
and the number of terms to be added or dropped determines the number of
cores that is actually used.
REML
a logical scalar controlling whether the restricted log-likelihood
should be extracted (default TRUE).
scale
a numeric, currently not used, see
extractAIC.
scope
defines the range of models examined in the stepwise search.
This should be either a single formula, or a list containing
components upper and lower, both formulae,
see step for details.
steps
a numeric with the maximum number of steps to be considered
(default is 1000), see step.
test
a character keyword specifying whether to compute the large
sample Chi-squared statistic (with asymptotic Chi-squared distribution)
or the finite sample F statistic (with approximate F distribution), see
waldtest.
trace
a numeric. If positive, information is printed during the
running of step, see step.
use.fitted.param
a logical scalar controlling whether fitted
values of param (and aniso are used as initial values
when variogram parameters are fitted afresh for adding and
dropping terms from the model (default TRUE). If equal
to FALSE then the initial values in object[["call"]] are
used.
vcov
a function for estimating the covariance matrix of the
regression coefficients, see waldtest.
verbose
a positive integer controlling logging of diagnostic
messages to the console during model fitting, see georob
(default 0).
warn
a logical scalar controlling whether warnings should be
suppressed.
...
additional arguments passed to methods (see in particular
waldtest.default).
Details
For a non-robust fit the function deviance returns the residual deviance
(\boldsymbol{Y} - \boldsymbol{X} \widehat{\boldsymbol{\beta}})^{\mathrm{T}}
(\widehat{\tau}^2 \boldsymbol{I} +
\boldsymbol{\Gamma}_{\widehat{\theta}})^{-1}
(\boldsymbol{Y} - \boldsymbol{X} \widehat{\boldsymbol{\beta}})
(see georobPackage for an explanation of the notation).
For a robust fit the deviance is not defined. The function then computes with a warning
the deviance of an equivalent Gaussian model with heteroscedastic nugget
\tau^2/\boldsymbol{w} where \boldsymbol{w} are
the “robustness weights” rweights, see georobObject.
logLik returns the maximized (restricted) log-likelihood. For
a robust fit, the log-likelihood is not defined. The function then
computes the (restricted) log-likelihood of an equivalent Gaussian model with
heteroscedastic nugget (see above).
The methods extractAIC, add1, drop1 and step
are used for stepwise model building.
If fixed=TRUE or
fixed.add1.drop1=TRUE (default) then the variogram parameters are
kept fixed at the values of object. For
fixed=FALSE or fixed.add1.drop1=FALSE the variogram
parameters are fitted afresh for each model tested by add1 and
drop1. Then either the variogram parameters in
object$initial.objects (use.fitted.param=FALSE) or the
fitted parameters of object (use.fitted.param=TRUE) are
used as initial values. For fixed.step=TRUE the variogram
parameters are not fitted afresh by step after the calls to
drop1 and add1 have been completed, unlike for
fixed.step=FALSE where the parameters are estimated afresh for
the new model that minimized AIC (BIC) in the previous step.
In addition, the functions of the R package multcomp can be used
to test general linear hypotheses about the fixed effects of the model.
Value
The method deviance.georob returns the deviance of the fitted
spatial linear model with the attributes log.det.covmat
containing the logarithm of the determinant of the covariance matrix
\tau^2 \boldsymbol{I} + \boldsymbol{\Gamma}_\theta
of the observations and optionally
log.det.xticovmatx with the logarithm of the determinant of
\boldsymbol{X}^\mathrm{T} (\tau^2
\boldsymbol{I} + \boldsymbol{\Gamma}_\theta)^{-1} \boldsymbol{X}
, when REML = true,
see Details above.
The method logLik.georob returns an object of class logLik
with the maximized (restricted) log-likelihood, see Details above
and logLik.
The method extractAIC.georob returns a numeric vector of length 2
with the first and second elements giving the equivalent degrees of
freedom and the (generalized) Akaike Information Criterion for the fitted
model fit.
The methods add1.georob and drop1.georob return objects of
class anova which are data.frames summarizing the
differences in fit between models. In addition to the customary
variables Df and AIC the output contains a logical variable
Converged which signals (non-)convergence when fitting the
respective sub-model.
The generic function step returns the stepwise selected model plus
optionally some additional attributes depending on the method.
The methods step.default and step.georob return the
stepwise-selected model with up to two additional components
(anova, keep), see step for details.
The method waldtest.georob returns an object of class anova
which contains the residual degrees of freedom, the difference in degrees
of freedom, Wald statistic (either "Chisq" or "F") and corresponding
p-value.
Author(s)
Andreas Papritz papritz@retired.ethz.ch.
See Also
georobPackage for a description of the model and a brief summary of the algorithms;
georob for (robust) fitting of spatial linear models;
georobObject for a description of the class georob;
profilelogLik for computing profiles of Gaussian likelihoods;
plot.georob for display of RE(ML) variogram estimates;
control.georob for controlling the behaviour of georob;
cv.georob for assessing the goodness of a fit by georob;
georobMethods for further methods for the class georob;
predict.georob for computing robust Kriging predictions;
lgnpp for unbiased back-transformation of Kriging prediction
of log-transformed data;
georobSimulation for simulating realizations of a Gaussian process
from model fitted by georob; and finally
sample.variogram and fit.variogram.model
for robust estimation and modelling of sample variograms.
Examples
data(meuse)
## Gaussian REML fit
r.logzn.reml <- georob(log(zinc) ~ sqrt(dist), data = meuse, locations = ~ x + y,
variogram.model = "RMexp",
param = c(variance = 0.15, nugget = 0.05, scale = 200),
tuning.psi = 1000)
summary(r.logzn.reml, correlation = TRUE)
deviance(r.logzn.reml)
logLik(r.logzn.reml)
waldtest(r.logzn.reml, .~. + ffreq)
step(r.logzn.reml, ~ sqrt(dist) + ffreq + soil)
## robust REML fit
if(interactive()){
## example is run only in interactive session because cpu times exceeds 5 s
r.logzn.rob <- update(r.logzn.reml, tuning.psi = 1)
deviance(r.logzn.rob)
logLik(r.logzn.rob)
logLik(r.logzn.rob, REML=TRUE)
step(r.logzn.rob, ~ sqrt(dist) + ffreq + soil, fixed.step=FALSE, trace=2)
}
georob documentation built on April 4, 2025, 2:11 a.m.
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| georobModelBuilding | R Documentation |
S3 Methods for Stepwise Building Fixed-Effects Models for Class georob
Description
This page documents the methods deviance,
logLik, extractAIC, add1, drop1,
step and waldtest for the class georob. The package
georob provides a generic step function and a default
method which is identical with the (non-generic) function
step.
Usage
## S3 method for class 'georob'
deviance(object, warn = TRUE, REML = FALSE, ...)
## S3 method for class 'georob'
logLik(object, warn = TRUE, REML = FALSE, ...)
## S3 method for class 'georob'
extractAIC(fit, scale = 0, k = 2, ...)
## S3 method for class 'georob'
add1(object, scope, scale = 0, test = c("none", "Chisq"), k = 2,
trace = FALSE, fixed = TRUE, use.fitted.param = TRUE, verbose = 0,
ncores = 1, ...)
## S3 method for class 'georob'
drop1(object, scope, scale = 0, test = c("none", "Chisq"), k = 2,
trace = FALSE, fixed = TRUE, use.fitted.param = TRUE, verbose = 0,
ncores = 1, ...)
step(object, ...)
## Default S3 method:
step(object, scope, scale = 0,
direction = c("both", "backward", "forward"), trace = 1,
keep = NULL, steps = 1000, k = 2, ...)
## S3 method for class 'georob'
step(object, scope, scale = 0,
direction = c("both", "backward", "forward"), trace = 1,
keep = NULL, steps = 1000, k = 2,
fixed.add1.drop1 = TRUE, fixed.step = fixed.add1.drop1,
use.fitted.param = TRUE, verbose = 0, ncores = 1, ...)
## S3 method for class 'georob'
waldtest(object, ..., vcov = NULL, test = c("F", "Chisq"),
name = NULL)
Arguments
object, fit |
an object of class |
direction |
a character keyword with the mode of stepwise search,
see |
fixed, fixed.add1.drop1 |
a logical scalar controlling whether the
variogram parameters are not adjusted when |
fixed.step |
a logical scalar controlling whether the variogram
parameters are not adjusted after having called |
k |
a numeric specifying the 'weight' of the equivalent degrees of
freedom (=: edf) part in the AIC formula, see
|
keep |
a filter function whose input is a fitted model object and the
associated |
name |
a function for extracting a suitable name/description from a
fitted model object. By default the name is queried by calling
|
ncores |
an integer specifying the number of cores used for
parallelized execution of |
REML |
a logical scalar controlling whether the restricted log-likelihood
should be extracted (default |
scale |
a numeric, currently not used, see
|
scope |
defines the range of models examined in the stepwise search.
This should be either a single formula, or a list containing
components |
steps |
a numeric with the maximum number of steps to be considered
(default is 1000), see |
test |
a character keyword specifying whether to compute the large
sample Chi-squared statistic (with asymptotic Chi-squared distribution)
or the finite sample F statistic (with approximate F distribution), see
|
trace |
a numeric. If positive, information is printed during the
running of |
use.fitted.param |
a logical scalar controlling whether fitted
values of |
vcov |
a function for estimating the covariance matrix of the
regression coefficients, see |
verbose |
a positive integer controlling logging of diagnostic
messages to the console during model fitting, see |
warn |
a logical scalar controlling whether warnings should be suppressed. |
... |
additional arguments passed to methods (see in particular
|
Details
For a non-robust fit the function deviance returns the residual deviance
(\boldsymbol{Y} - \boldsymbol{X} \widehat{\boldsymbol{\beta}})^{\mathrm{T}}
(\widehat{\tau}^2 \boldsymbol{I} +
\boldsymbol{\Gamma}_{\widehat{\theta}})^{-1}
(\boldsymbol{Y} - \boldsymbol{X} \widehat{\boldsymbol{\beta}})
(see georobPackage for an explanation of the notation).
For a robust fit the deviance is not defined. The function then computes with a warning
the deviance of an equivalent Gaussian model with heteroscedastic nugget
\tau^2/\boldsymbol{w} where \boldsymbol{w} are
the “robustness weights” rweights, see georobObject.
logLik returns the maximized (restricted) log-likelihood. For
a robust fit, the log-likelihood is not defined. The function then
computes the (restricted) log-likelihood of an equivalent Gaussian model with
heteroscedastic nugget (see above).
The methods extractAIC, add1, drop1 and step
are used for stepwise model building.
If fixed=TRUE or
fixed.add1.drop1=TRUE (default) then the variogram parameters are
kept fixed at the values of object. For
fixed=FALSE or fixed.add1.drop1=FALSE the variogram
parameters are fitted afresh for each model tested by add1 and
drop1. Then either the variogram parameters in
object$initial.objects (use.fitted.param=FALSE) or the
fitted parameters of object (use.fitted.param=TRUE) are
used as initial values. For fixed.step=TRUE the variogram
parameters are not fitted afresh by step after the calls to
drop1 and add1 have been completed, unlike for
fixed.step=FALSE where the parameters are estimated afresh for
the new model that minimized AIC (BIC) in the previous step.
In addition, the functions of the R package multcomp can be used to test general linear hypotheses about the fixed effects of the model.
Value
The method deviance.georob returns the deviance of the fitted
spatial linear model with the attributes log.det.covmat
containing the logarithm of the determinant of the covariance matrix
\tau^2 \boldsymbol{I} + \boldsymbol{\Gamma}_\theta
of the observations and optionally
log.det.xticovmatx with the logarithm of the determinant of
\boldsymbol{X}^\mathrm{T} (\tau^2
\boldsymbol{I} + \boldsymbol{\Gamma}_\theta)^{-1} \boldsymbol{X}
, when REML = true,
see Details above.
The method logLik.georob returns an object of class logLik
with the maximized (restricted) log-likelihood, see Details above
and logLik.
The method extractAIC.georob returns a numeric vector of length 2
with the first and second elements giving the equivalent degrees of
freedom and the (generalized) Akaike Information Criterion for the fitted
model fit.
The methods add1.georob and drop1.georob return objects of
class anova which are data.frames summarizing the
differences in fit between models. In addition to the customary
variables Df and AIC the output contains a logical variable
Converged which signals (non-)convergence when fitting the
respective sub-model.
The generic function step returns the stepwise selected model plus
optionally some additional attributes depending on the method.
The methods step.default and step.georob return the
stepwise-selected model with up to two additional components
(anova, keep), see step for details.
The method waldtest.georob returns an object of class anova
which contains the residual degrees of freedom, the difference in degrees
of freedom, Wald statistic (either "Chisq" or "F") and corresponding
p-value.
Author(s)
Andreas Papritz papritz@retired.ethz.ch.
See Also
georobPackage for a description of the model and a brief summary of the algorithms;
georob for (robust) fitting of spatial linear models;
georobObject for a description of the class georob;
profilelogLik for computing profiles of Gaussian likelihoods;
plot.georob for display of RE(ML) variogram estimates;
control.georob for controlling the behaviour of georob;
cv.georob for assessing the goodness of a fit by georob;
georobMethods for further methods for the class georob;
predict.georob for computing robust Kriging predictions;
lgnpp for unbiased back-transformation of Kriging prediction
of log-transformed data;
georobSimulation for simulating realizations of a Gaussian process
from model fitted by georob; and finally
sample.variogram and fit.variogram.model
for robust estimation and modelling of sample variograms.
Examples
data(meuse)
## Gaussian REML fit
r.logzn.reml <- georob(log(zinc) ~ sqrt(dist), data = meuse, locations = ~ x + y,
variogram.model = "RMexp",
param = c(variance = 0.15, nugget = 0.05, scale = 200),
tuning.psi = 1000)
summary(r.logzn.reml, correlation = TRUE)
deviance(r.logzn.reml)
logLik(r.logzn.reml)
waldtest(r.logzn.reml, .~. + ffreq)
step(r.logzn.reml, ~ sqrt(dist) + ffreq + soil)
## robust REML fit
if(interactive()){
## example is run only in interactive session because cpu times exceeds 5 s
r.logzn.rob <- update(r.logzn.reml, tuning.psi = 1)
deviance(r.logzn.rob)
logLik(r.logzn.rob)
logLik(r.logzn.rob, REML=TRUE)
step(r.logzn.rob, ~ sqrt(dist) + ffreq + soil, fixed.step=FALSE, trace=2)
}
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