Thanks for your summary, Hank. On 9/7/06, Martin Henry H. Stevens <[EMAIL PROTECTED]> wrote: > Dear lmer-ers, > My thanks for all of you who are sharing your trials and tribulations > publicly.
> I was hoping to elicit some feedback on my thoughts on denominator > degrees of freedom for F ratios in mixed models. These thoughts and > practices result from my reading of previous postings by Doug Bates > and others. > - I start by assuming that the appropriate denominator degrees lies > between n - p and and n - q, where n=number of observations, p=number > of fixed effects (rank of model matrix X), and q=rank of Z:X. I agree with this but the opinion is by no means universal. Initially I misread the statement because I usually write the number of columns of Z as q. It is not easy to assess rank of Z:X numerically. In many cases one can reason what it should be from the form of the model but a general procedure to assess the rank of a matrix, especially a sparse matrix, is difficult. An alternative which can be easily calculated is n - t where t is the trace of the 'hat matrix'. The function 'hatTrace' applied to a fitted lmer model evaluates this trace (conditional on the estimates of the relative variances of the random effects). > - I then conclude that good estimates of P values on the F ratios lie > between 1 - pf(F.ratio, numDF, n-p) and 1 - pf(F.ratio, numDF, n-q). > - I further surmise that the latter of these (1 - pf(F.ratio, numDF, > n-q)) is the more conservative estimate. > > When I use these criteria and compare my "ANOVA" table to the results > of analysis of Helmert contrasts using MCMC sample with highest > posterior density intervals, I find that my conclusions (e.g. factor > A, with three levels, has a "significant effect" on the response > variable) are qualitatively the same. > Comments? I would be happy to re-institute p-values for fixed effects in the summary and anova methods for lmer objects using a denominator degrees of freedom based on the trace of the hat matrix or the rank of Z:X if others will volunteer to respond to the "these answers are obviously wrong because they don't agree with <whatever> and the idiot who wrote this software should be thrashed to within an inch of his life" messages. I don't have the patience. ______________________________________________ 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 and provide commented, minimal, self-contained, reproducible code.