[R] lmer() vs. lme() gave different variance component estimates

[array chip]

Thank you Peter and Ben for your comments.

John


----- Original Message ----
From: Peter Dalgaard <pdalgd at gmail.com>
To: array chip <arrayprofile at yahoo.com>
Cc: r-help at r-project.org; r-sig-mixed-models at r-project.org
Sent: Mon, September 20, 2010 12:28:43 PM
Subject: Re: [R] lmer() vs. lme() gave different variance component estimates

On 09/20/2010 08:09 PM, array chip wrote:
> 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?

It is only exactly true for a balanced design, although it can be a
practical expedient in nearly-balanced cases, especially if there is a
clearly dominant animal variation. In strongly unbalanced data, you get
reduced efficiency because animals with less data should be downweighted
(not proportionally if there is substantial between-animal variation,
though). And of course the whole thing relies on the fact that you have
individuals nested in treatment (no animals had multiple treatments)

> 
> 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?

Not too far off the mark. In more complex cases, there is the advantage
that the mixed model helps figure out a sensible analysis for you.


> 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?

I think Doug's view is that DFs are not _reliably_estimated_ with any of
the current procedures. In the balanced cases, they are very well
defined (well, give or take the issues with "negative variances"), and I
would expect glht() to give meaningful results. Do check the residuals
for at least approximate normality, though.


> 
> Thank you very much!
> 
> John
> 
> 
> 
> 
> 
> ----- Original Message ----
> From: Peter Dalgaard <pdalgd at gmail.com>
> To: array chip <arrayprofile at yahoo.com>
> Cc: r-help at r-project.org; r-sig-mixed-models at 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.mes at cbs.dk  Priv: PDalgd at gmail.com