---------- Forwarded message ----------
From: H c <harlancampbell@gmail.com>
Date: Tue, Apr 14, 2009 at 1:02 PM
Subject: Re: [R-sig-ME] Numerical methods used to compute correlation
coefficients
To: Douglas Bates <bates@stat.wisc.edu>


Thank you for the quick response.
when I refer to "correlation parameters", I mean the "generally small set of
parameters \lambda" that parametrize the \Lambda_{i} Variance-Covariance
matrix.

For example, one has time series data such that every subject has been
observed at 4 time points.  One wishes to model this using an AR(1)
correlation structure within the mixed model.
the AR(1) is parametrized by a fixed parameter, \phi :

lme(y~X, random=~1|ID, method="ML", data=data,
correlation=corAR1(0.5,form=~X,fixed=FALSE))


Since there is no closed form solution for the maximum-likelihood estimate
of \phi.  what numerical methods are used to arrive at the given estimate?

Hopefully this has clarified my question.
Thanks again,

Harlan


On Tue, Apr 14, 2009 at 12:37 PM, Douglas Bates <bates@stat.wisc.edu> wrote:

> On Tue, Apr 14, 2009 at 9:20 AM, H c <harlancampbell@gmail.com> wrote:
> > I have have already posted the following question:  What numerical
> methods
> > are used in nlme to estimate correlation parameters?
> > I was referred to the Pinheiro and Bates book.  Unfortunately, on p. 202,
> > section 5.1.1, under the title "Estimation and Computational Methods", no
> > description on a numerical method is provided.  (When the data is
> > transformed to work with the profiled likelihood(y->ystar), one needs the
> > parameters that define Lambda.  How are these parameters estimated?)
>
> I'm not sure what you mean by "correlation parameters".  If you mean
> the correlation parameters in the unconditional distribution of the
> random effects then those are estimated by maximum likelihood (ML) or
> residual maximum likelihood (REML).  The profiled deviance or the
> profiled REML criterion is evaluated with respect to a transformed set
> of parameters and this value is optimized.
>

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