[R-sig-ME] Nested random effect within fixed effect factor?

[ONKELINX, Thierry]

Kristofor,

Don't forget that you have only 10 sites. That gives you an estimate of the random intercept variance but a rather poor estimate. The ratio of the sample variance and the true variance follows a Chisq distribution. With only 10 sites you get very wide confidence intervals on the variance. With 5 sites the get even wider, thus making a comparison between then irrelevant. You need a lot of data to get decent variance estimates.

CI.ratio = chisq(c(0.025, 0.975), df = n - 1) / (n - 1)

n = 5: c(0.12, 2.8)
n = 10: c(0.3, 2.1)
n = 30: c(0.55, 1.58)
n = 100: c(0.74, 1.30)
n = 200: c(0.81, 1.21)

So I would not even try to model a different random effect variance per treatment with your dataset.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx op inbo.be
www.inbo.be

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-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces op r-project.org [mailto:r-sig-mixed-models-bounces op r-project.org] Namens David Duffy
Verzonden: woensdag 31 juli 2013 8:15
Aan: Kristofor Voss
CC: r-sig-mixed-models op r-project.org
Onderwerp: Re: [R-sig-ME] Nested random effect within fixed effect factor?

On Wed, 31 Jul 2013, Kristofor Voss wrote:

> Thanks. Yes this partitions the error variance, but not the random
> effect variance. That part is working fine (and in fact matches what I
> get from running both subsets). But still curious about the random
> effects being different.

I'm not sure you're right in characterizing it that way.  My simple-minded understanding (I would be grateful for correction) is that you can get equivalent models by either modeling the off-diagonal covariances for Z or for e, since here you don't have an informative design (some clusters or individuals receiving both treatments).


| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD op qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v

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