Is PROC GLM or PROC MIXED appropriate for a one-way within-subjects RM ANOVA design ?

[lvm]

Actually, since you are using the beta distribution, you are treating you data as continuous, but bound by 0 and 1. (I missed this before). So, the idea of overdispersion is not relevant. That is, the beta has a scale parameter that is estimated, so there is no real relevance to the chi-square/df statistic in you case (the way I am looking at it now).

[stan]

lvm, I actually use binomial distribution... Well, Steve mentioned and I used beta as a counterpart for the binomial.

But I was advised at stats.stackexchange.com/q/11980 to use the binomial distribution. I admit it sounds

unconvincingly but cbeleites put some arguments for the choice (comment on Jun 2 '13).

[lvm]

Then my original comments are appropriate.

[stan]

Dear lvm,

you indicated that

The NMSIMP method does not use derivatives in the optimization.

Could you please elaborate on this in more or less simple terms?

stan

[lvm]

I can't do it in simple terms.In general, mixed models require an iterative approach to find the parameters that give the maximum value of the log likelihood (or minimum value of -2 times the log likelihood). Most optimization approaches use either the first or second derivative of the log likelihood with respect to the parameters in the iterative process. The Nelder-Mead simplex method (NMSIMP), however, does not use derivatives. It may take many-many iterations to converge, and the whole process can be very slow. It may become impossibly slow with many data points. But it is one of the valid methods. The second derivatives are calculated at the end of the optimization in order to estimate variances. See the Shared Concepts and Topics chapter in the SAS/STAT User's Guide (under NLOPTIONS) to learn more.

[stan]

It became clearer. Thank you.