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.