[R-sig-ME] Numerical methods used to compute correlation coefficients

[Douglas Bates]

On Tue, Apr 14, 2009 at 9:20 AM, H c <harlancampbell at 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.