[R-sig-ME] Effective sample size

[Douglas Bates]

On Mon, Jul 19, 2010 at 4:27 AM, John Maindonald
<john.maindonald at anu.edu.au> wrote:
> Does anyone know of an implementation of the Effective Sample Size
> methodology that is described in
> <<<
> The Effective Sample Size and an Alternative Small-Sample Degrees-of-Freedom Method
> by: Christel Faes, Geert Molenberghs, Marc Aerts, Geert Verbeke, Michael G. Kenward
> The American Statistician, Vol. 63, No. 4. (2009), pp. 389-399.
>>>> ?
>
> The key requirement, as I understand the paper, is to calculate a variance for the predicted
> value, for each observation.

Sorry to come back to this question after so long John (I was at the
useR!2010 conference followed by vacation) but I think that the trick
is first to define the variance for the predicted value.  I haven't
read the paper myself and probably should not speculate on how the
methods are being formulated but I do note that often there is an
preconception that it should be possible to incorporate the
variability from the random effects or from their conditional means
along with the variability of the estimators of the fixed-effects
parameters into some kind of variance for the predicted values.  It is
not clear to me how this would be done if one reverts to the
definition of the probability model, which is the only way I know of
keeping the theory straight.  As you may know I tend to think of the
fixed-effects as entering into the definition of the conditional
distribution of the response, given the random effects, and the
variance-component parameters as being part of the definition of the
unconditional distribution of the random effects.  To me it is rather
tricky to decide how all the "sources of variability" could be
incorporated into the variance of a predicted value.