[R-sig-ME] Calculating an Intraclass Correlation Coefficient or Repeatability estimate from lmer() output

[Jarrod Hadfield]

Hi,

You have the components the wrong way round:  the ID variance is the  
among groups, and the Residual variance is the within groups, but  
other than that it looks fine.

Jarrod
On 14 Oct 2009, at 13:24, amelie lescroel wrote:

> Dear all,
>
> I am interested in calculating an Intraclass Correlation Coefficient  
> (ICC) or Repeatability estimate from a mixed model output (lmer()).  
> Lessels & Boag (1987) defined repeatability as the intraclass  
> correlation coefficient based on variance components derived from a  
> one-way anova:
> r = among-groups variance components / (within-group variance  
> components + among-group variance components)
> What I would like to know is where/how to find these variance  
> components in a lmer() output.
>
> Specifically, we measured foraging efficiency (CPUE) of birds during  
> 10 consecutive years. We have several measures per bird for each  
> year and the same birds were measured over multiple years. What I  
> would like to get is an estimate of the intra-individual consistency  
> of foraging efficiency over time. And I thought that the ICC or  
> repeatability would be this estimate (recently used in the same  
> manner in Lang et al. 2009 Ecology 90(9): 2513-2523).
>
> Let’s run a model with the ID of the birds as a random factor:
>
>> (fm1 <- lmer(log.CPUE~(1|ID)))
> Linear mixed model fit by REML
> Formula: log.CPUE ~ (1 | ID)
>   AIC   BIC logLik deviance REMLdev
> -1144 -1126  575.2    -1158   -1150
> Random effects:
> Groups   Name        Variance Std.Dev.
> ID       (Intercept) 0.010292 0.10145
> Residual             0.036602 0.19132
> Number of obs: 3320, groups: ID, 341
>
> Fixed effects:
>            Estimate Std. Error t value
> (Intercept)   0.3484     0.0068   51.24
>
> In this case, is the within-individual variance = 0.010 and the  
> among-individuals variance = 0.037?
>
> Thanks for your help,
>
> Amelie
>
> Amélie Lescroël
> Seabird ecologist
> URU 420, Université de Rennes I - Service du Patrimoine Naturel,  
> Museum National d’Histoire Naturelle
> 263 Av. du Gal Leclerc
> 35042 Rennes Cedex
> France
>
>
>
>
> __________ Information from ESET Mail Security, version of virus  
> signature database 4506 (20091014) __________
>
> The message was checked by ESET Mail Security.
> http://www.eset.com
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models


-- 
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.