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

amelie lescroel amelie.lescroel at cebc.cnrs.fr
Wed Oct 14 14:24:44 CEST 2009

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,


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

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