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
Am?lie Lescro?l
Seabird ecologist
URU 420, Universit? de Rennes I - Service du Patrimoine Naturel,
Museum National d?Histoire Naturelle
263 Av. du Gal Leclerc
35042 Rennes Cedex
France
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