qscoring: Quasi-scoring iteration

Description Usage Arguments Details Value Author(s) See Also Examples

View source: R/qsOpt.R

Description

The function solves the quasi-score equation by a root finding algorithm similar to Fisher's scoring iteration.

Usage

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qscoring(qsd, x0, opts = list(), Sigma = NULL, ..., inverted = FALSE,
  check = TRUE, cvm = NULL, Iobs = TRUE, pl = 0L, verbose = FALSE)

Arguments

qsd

object of class QLmodel

x0

(named) numeric vector, the starting parameter

opts

quasi-scoring options, see details

Sigma

a pre-specified variance matrix estimate

...

further arguments passed to function covarTx

inverted

currently ignored

check

logical, TRUE (default), whether to check input arguments

cvm

list of covariance models for cross-validation (see prefitCV)

Iobs

logical, FALSE default, whether to compute observed quasi-information matrix

pl

numeric, print level, use pl>0 to give intermediate output

verbose

FALSE (default), otherwise print intermediate output

Details

The function implements a step-length controlled quasi-scoring iteration with simple bound constraints (see, e.g. [1,3]) specifically tailored for quasi-likelihood parameter estimation. Due to the typical nonconvex nature of the (unknown and not further specified) quasi-likelihood 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 quasi-deviance 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.

Quasi-scoring under uncertainty

The quasi-scoring iteration covers both kinds of prediction variances, kriging-based and those by a CV approach, which account for the uncertainty induced by the quasi-score 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 quasi-score function.

Opposed to this, the user also has the option to carry out a "pure version" of quasi-scoring without accounting for these errors. This can be set earlier as an option in QLmodel. 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:

Value

List of results of quasi-scoring iteration.

convergence

integer, why scoring iterations stopped

message

string, corrsponding to 'convergence'

iter

number of iterations

value

quasi-deviance value

par

solution vector

score

quasi-score vector

I

quasi-information matrix

start

starting point

method

simply: "qscoring"

criterion

equal to "qle"

Author(s)

M. Baaske

See Also

prefitCV

Examples

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data(normal)
QS <- qscoring(qsd,x0=c("mu"=3.5,"sigma"=0.5),
         opts=list("score_tol"=1e-4))

mbaaske/qle documentation built on Feb. 3, 2018, 11:02 a.m.