[R-sig-ME] Extracting variances of the estimated variance components in lme4

[Ben Bolker]

Freedom Gumedze <Freedom.Gumedze at ...> writes:

> Douglas and Thierry,
> 
> Many thanks Douglas for the advice. I will look at the suggestion by
> Douglas when the URL is visible.
> The omission of the option for the standard errors of the estimated
> variances (or std deviations) is understandable to avoid their 'abuse
> e.g. in significance testing'. However, they should be available (if
> needed) as they can be obtained from the inverse of information matrix
> for the var. components.

  It's not quite that easy, because the variance components are not
estimated on the scale of variances or standard deviations, but on the
Cholesky scale, so (depending on the model) the information matrix of
the 'theta' parameter vector (a concatenated vector of the lower triangles
of the Cholesky factors) may not be easy to translate to the
information matrix of the standard deviations or variances.  I posted
some code earlier in response to a query of Josh Wiley's, based on the
development version of lme4 (sorry), that extracts the deviance function
and wraps it in a function that transforms standard deviations to 
the Cholesky-factor parameterization -- combining this with finite-difference
approximations of second derivatives (e.g. from the numDeriv package)
will give the standard errors of the estimated parameters, if you want
them.

  I have the intention of including this stuff in a skull-and-crossbones-marked
section of an "lme4-extras" vignette (if Doug lets me).  The vignette is
in progress, I can send it on request.

  Ben Bolker