Description Usage Arguments Details Value Author(s) See Also Examples
The function numerically solves the quasiscore equation by a root finding algorithm similar to Fisher's scoring method.
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qsd 
object of class 
x0 
(named) numeric vector, the starting parameter 
opts 
quasiscoring options, see details 
Sigma 
a prespecified variance matrix estimate 
... 
further arguments passed to the function 
inverted 
currently ignored 
check 
logical, 
cvm 
list of covariance models for crossvalidation (see 
Iobs 
logical, 
pl 
numeric, print level, use 
verbose 

The function implements a steplength controlled quasiscoring iteration with simple bound constraints (see also [1,3]) specifically tailored for quasilikelihood parameter estimation. Due to the typical nonconvex nature of the (unknown and not further specified) quasilikelihood function as an objective function one needs some kind of globalization strategy in order to stabilize the descent step and to avoid a premature termination. Therfore, we use the quasideviance function as a monitor function (see vignette) though it does not inherit all of the appreciable properties of a true objective function such as among others, for example, identifying appropriate descent directions. However, these are general numerical obsticles in case of pure root finding algorithms and need to be addressed elsewhere.
The quasiscoring iteration includes both kinds of prediction variances, krigingbased and those derived from a crossvalidation (CV) approach,
which account for the uncertainty induced by the quasiscore approximation model. By default kriging variances
are included in the computation during all iterations. If fitted covariance models 'cvm
' are supplied by the user
in advance (see prefitCV
), the variances of prediction errors of each statistic are separately evaluated by the proposed CV
approach for each new point. For the price of relatively high computational costs those prediction variances
are intended to increase the robustness against false roots due to simulation and approximation errors of the quasiscore function.
Opposed to this, the user also has the option to carry out a "pure version" of quasiscoring without accounting for
these errors. This can be set earlier as an option in QLmodel
using dual kriging prediction.
See also covarTx
and mahalDist
for details on how to choose the variance matrix approximation of the statistics.
The following algorithmic options, which can be set by 'opts
', are available:
ftol_stop
: minimum value of the quasideviance for stopping the scoring iteration
ftol_abs
: minimum value of the quasideviance which is used as a reference value for a local minimizer
xtol_rel
, ftol_rel
: see qle
grad_tol
: upper bound on the quasiscore vector components,
testing for a local minimum of the quasideviance in case of a line search failure
score_tol
: upper bound on the quasiscore vector components, testing for an approximate root
maxiter
: maximum allowed number of iterations
xscale
: numeric, default is vector of 1, typical magnitudes of vector components of 'x0
', e.g. the order of upper bounds of the parameter space
fscale
: numeric, default is vector of 1, typical magnitudes of quasiscore components
pl
: print level (>=0), use pl
=10 to print individual
iterates and further values
List of results of quasiscoring iteration with elements:
convergence 
integer, why scoring iterations stopped 
message 
string, corrsponding to ' 
iter 
number of iterations 
value 
quasideviance value 
par 
solution vector 
score 
quasiscore vector 
I 
quasiinformation matrix 
start 
starting point 
method 
simply: " 
criterion 
equal to " 
M. Baaske
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