From a quick look at the paper in the SAS proceedings, the simulations seem limited to nested designs. The major problems are with repeated measures designs where the error structure is not compound symmetric, which lme4 does not at present handle (unless I have missed something). Such imbalance as was investigated was not a serious issue, at least for the Kenward and Roger degree of freedom calculations.
The paper ends by commenting that "research should continue". What may be even more important is to educate users to think carefully about any df that they are presented with, and to be especially sceptical when designs are not approximately balanced nested designs and/or there are repeated measures error structures that are not compound symmetric. It is also necessary to consider how well the analysis reflects matters on which there may be existing good evidence. Suppose in Ronaldo's case that he'd previously run a number of experiments with very similar plots and observation al units, and with comparable treatments and outcome measures. If the plot 1 SD estimate (i.e., at the level of experimental units) had never been larger than 0.01, with the SD for observational units always in a range of 2 to 20, I'd take this as licence to ignore the variance at the plot 1 level. It would be nice to be able to build in such prior information more formally, probably via a modified version of mcmcsamp(). [Some people are never satisfied, You've written a great piece of software, and users reward you by complaining that they want even more!] John Maindonald. On 1 Jan 2006, at 10:00 PM, [EMAIL PROTECTED] wrote: > From: Dave Atkins <[EMAIL PROTECTED]> > Date: 1 January 2006 1:40:45 AM > To: r-help@stat.math.ethz.ch > Subject: Re: [R] lme X lmer results > > > > Message: 18 > Date: Fri, 30 Dec 2005 12:51:59 -0600 > From: Douglas Bates <[EMAIL PROTECTED]> > Subject: Re: [R] lme X lmer results > To: John Maindonald <[EMAIL PROTECTED]> > Cc: r-help@stat.math.ethz.ch > Message-ID: > <[EMAIL PROTECTED]> > Content-Type: text/plain; charset=ISO-8859-1 > > On 12/29/05, John Maindonald <[EMAIL PROTECTED]> wrote: > > >> Surely there is a correct denominator degrees of freedom if the > design > >> is balanced, as Ronaldo's design seems to be. Assuming that he has > >> specified the design correctly to lme() and that lme() is > getting the df > >> right, the difference is between 2 df and 878 df. If the t- > statistic > >> for the > >> second level of Xvar had been 3.0 rather than 1.1, the difference > >> would be between a t-statistic equal to 0.095 and 1e-6. In a > design > >> where there are 10 observations on each experimental unit, and all > >> comparisons are at the level of experimental units or above, df for > >> all comparisons will be inflated by a factor of at least 9. > > Doug Bates commented: > > I don't want to be obtuse and argumentative but I still am not > convinced that there is a correct denominator degrees of freedom for > _this_ F statistic. I may be wrong about this but I think you are > referring to an F statistic based on a denominator from a different > error stratum, which is not what is being quoted. (Those are not > given because they don't generalize to unbalanced designs.) > > This is why I would like to see someone undertake a simulation study > to compare various approaches to inference for the fixed effects terms > in a mixed model, using realistic (i.e. unbalanced) examples. > > Doug-- > > Here is a paper that focused on the various alternatives to > denominator degrees of freedom in SAS and does report some > simulation results: > > http://www2.sas.com/proceedings/sugi26/p262-26.pdf > > Not sure whether it argues convincingly one way or the other in the > present discussion. > > cheers, Dave > > -- > Dave Atkins, PhD > [EMAIL PROTECTED] > ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html