Thank you Peter for your explanation of relationship between aov and lme. It makes perfect sense.
When you said "you might have computed the average of all 8 measurements on each animal and computed a 1-way ANOVA" for treatment effect, would this be the case for balanced design, or it is also true for unbalanced data? Another question is if 1-way ANOVA is equivalent to mixed model for testing treatment effect, what would be reason why mixed model is used? Just to estimate the variance components? If the interest is not in the estimation of variance components, then there is no need to run mixed models to test treatment effects? And my last question is I am glad to find that glht() from multcomp package works well with a lmer() fit for multiple comparisons. Given Professor Bates's view that denominator degree's of freedom is not well defined in mixed models, are the results from glht() reasonable/meaningful? If not, will the suggested 1-way ANOVA used together with glht() give us correct post-hoc multiple comparsion results? Thank you very much! John ----- Original Message ---- From: Peter Dalgaard <pda...@gmail.com> To: array chip <arrayprof...@yahoo.com> Cc: r-help@r-project.org; r-sig-mixed-mod...@r-project.org Sent: Sat, September 18, 2010 1:35:45 AM Subject: Re: [R] lmer() vs. lme() gave different variance component estimates For a nested design, the relation is quite straightforward: The residual MS are the variances of sample means scaled to be comparable with the residuals (so that in the absense of random components, all MS are equal to within the F-ratio variability). So to get the id:eye variance component, subtract the Within MS from the id:eye MS and divide by the number of replicates (4 in this case since you have 640 observations on 160 eyes) (14.4 - 0.01875)/4 = 3.59, and similarly, the id variance is the MS for id minus that for id:eye scaled by 8: (42.482-14.4)/8 = 3.51. I.e. it is reproducing the lmer results above, but of course not those from your original post. (Notice, by the way, that if you are only interested in the treatment effect, you might as well have computed the average of all 8 measurements on each animal and computed a 1-way ANOVA). -- Peter Dalgaard Center for Statistics, Copenhagen Business School Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org 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.
