This function is generic. It performs adjustment of the loglikelihood
associated with fitted model objects, following
Chandler and Bate (2007).
Certain classes of extreme value model objects are supported automatically.
For details see the alogLik help pages for the packages:
evd,
evir,
extRemes,
fExtremes,
ismev,
mev,
POT,
texmex.
User-supplied objects can also be supported: the requirements for these
objects are explained in Details.
alogLik(x, cluster = NULL, use_vcov = TRUE, ...)A fitted model object with certain associated S3 methods. See Details.
A vector or factor indicating from which cluster the
respective loglikelihood contributions from loglik originate.
This must have the same length as the vector returned by the
logLikVec method for an object like x.
If cluster is not supplied (i.e. is NULL) then it is
assumed that each observation forms its own cluster.
See Details.
A logical scalar. Should we use the vcov S3 method
for x (if this exists) to estimate the Hessian of the independence
loglikelihood to be passed as the argument H to
adjust_loglik?
Otherwise, H is estimated inside
adjust_loglik using
optimHess.
An object inheriting from class "chandwich". See
adjust_loglik.
If x is one of the supported models then class(x) is a
vector of length 5. The first 3 components are
c("lax", "chandwich", "name_of_package"), where
"name_of_package" is the name of the package from which the input
object x originated. The remaining 2 components depend on the
model that was fitted. See the documentation of the relevant package
for details:
evd,
evir,
extRemes,
fExtremes,
ismev,
mev,
POT,
texmex.
Otherwise, class(x) is c("lax", "chandwich", class(x)).
Objects returned from `aloglik` have `anova`, `coef`, `confint`, `logLik`, `nobs`, `plot`, `print`, `summary` and `vcov` methods.
Object x must have the following S3
methods:
logLikVec: returns a vector of the contributions to the
independence loglikelihood from individual observations;
coef: returns a vector of model coefficients, see
coef;
nobs: returns the number of (non-missing) observations
used in a model fit, see nobs;
and may have the following S3 methods
vcov: returns the estimated variance-covariance matrix of
the (main) parameters of a fitted model, see
vcov;
estfun: returns an \(n x k\) matrix, in which each
column gives the derivative of the loglikelihood at each of \(n\)
observation with respect to the \(k\) parameters of the model, see
estfun.
Loglikelihood adjustment is performed using the
adjust_loglik function in the
chandwich package.
The relevant arguments to adjust_loglik, namely
loglik, mle, H and V, are created based on the class of
the object x.
If a vcov method is not available, or if use_vcov = FALSE,
then the variance-covariance matrix of the MLE (from which H is
calculated) is estimated inside adjust_loglik
using optimHess.
The sandwich package is used to estimate the variance matrix
V of the score vector: meat is used if
cluster = NULL; meatCL is used if
cluster is not NULL.
If cluster is NULL then any arguments of
meatCL present in … will be ignored.
Similarly, if cluster is not NULL then any arguments of
meat present in … will be ignored.
meat and meatCL
require an estfun method to be available, which,
in the current context, provides matrix of score contributions.
If a bespoke estfun method is not provided then this is constructed
by estimating the score contributions using jacobian.
Chandler, R. E. and Bate, S. (2007). Inference for clustered data using the independence loglikelihood. Biometrika, 94(1), 167-183. http://doi.org/10.1093/biomet/asm015
Zeleis (2006) Object-Oriented Computation and Sandwich Estimators. Journal of Statistical Software, 16, 1-16. http://doi.org/10.18637/jss.v016.i09
summary.chandwich,
plot.chandwich,
confint.chandwich,
anova.chandwich,
coef.chandwich,
vcov.chandwich
and logLik.chandwich
for S3 methods for objects of class "chandwich".
conf_region for confidence regions for
pairs of parameters.
adjust_loglik in the
chandwich package to adjust a user-supplied
loglikelihood.