mlefn {missreg}R Documentation

A modified Newton maximiser

Description

A function to maximise, minimise or find stationary values for a (general) function. It was originally written to maximize a loglikelihood function so that is the language that is employed.

mlefn.control and mlefn.control.inner supply parameter values to control the iterative process and reporting. They differ only in their defaults.

Usage

mlefn(theta, loglkfn, control=mlefn.control(...), ...)

mlefn.control(messg="", niter=20, tol=1e-08, guide="uphill",
      print.progress=2, max.eigenrat=0.05, n.earlyit=0,
      constrain="no", fixed=NULL, Aconstrain=NULL, 
      cconstrain=NULL, ...)

mlefn.control.inner(messg="Inner:", niter=20, tol=1e-08, 
      guide="auto", print.progress=0, max.eigenrat=0.05, 
      n.earlyit=0, constrain="no", fixed=NULL, 
      Aconstrain=NULL, cconstrain=NULL, ...)

Arguments

theta Starting values for the parameters of the loglikelhood function.
loglkfn An inner function to compute the loglikelihood and its derivatives. The values returned by this function must be a list with loglk, score and inf.
messg A labelling string to be printed as a part of warnings etc. Useful with nested calls to mlefn.
niter Maximum number of iterations used. The default is 20.
tol Level of tolerance for checking the convergence.
guide Specification of the direction for convergence with the following choices:
"uphill"
– seek a maximum;
"downhill"
– seek a minimum;
"no"
– straight Newton approach without using loglikelihood values to guide the search.
"auto"
– only used in mlefn.control.inner when the inner function loglkfn requires a call to mlefn itself and we want it to determine and supply a legitmate value for that (inner) call.
print.progress A numeric value used to control the printing of error messages (if any); 0 should be used if no printing is required.
max.eigenrat An argument used in the inner function greenstadt.step to control the eigenvalues of the information matrix. This is the Greenstadt modification described in page 601 of Seber and Wild (1989).
n.earlyit Number of iterations to be treated as "early"; The default is 0.
constrain Specification of constrain on the parameter estimates with the following choices:
"no"
– no constrains;
"fix"
– fix some of the parameters at their starting values;
fixed A vector specifying the parameters to be fixed, indicated by their orders in theta. Used only if constrain="fix".
Aconstrain an I matrix with number of rows equal to the number of "fixed" parameters. Used only if constrain="fix".
cconstrain A vector specifying the values of those "fixed" parameters.
Used only if constrain="fix".
... Further arguments passed to or from related functions.

Details

This is the base function to maximise, minimise or find stationary values for theta using the provided loglkfn function. All semi-parametric maximum likelihood approaches we have proposed in missreg library require this function to obtain maximum likelihood estimates of parameters. See "Description of the missreg Library" for more details.

Value

A list with the following components.

theta Updated parameter estimates at this iteration.
loglk Log-likelihood obtained from the current theta values.
score Score vector obtained from the current theta values.
inf Observed information matrix obtained from the curent theta values.
constrscore Constrained score vector if constrain="fix"; otherwise NULL.
constrinf Constrained observed information matrix if constrain="fix"; otherwise NULL.
counter Number of iterations performed.
error A numeric value indicating the types of errors during iterations; a value of 0 indicates no error.

Author(s)

Chris Wild, Yannan Jiang

References

Nonlinear Regression, Seber and Wild, 1989. Wiley: New York.
Description of the missreg Library, Wild and Jiang, 2007.

[Package missreg version 2.0.1 Index]