[R] icc from GLMM?

From: Shinichi Nakagawa <S.Nakagawa_at_sheffield.ac.uk>
Date: Fri, 08 Jun 2007 10:38:38 +0100


Dear R users

I would like to ask a question regarding to icc (intraclass correlation) or many biologists refer it to as repeatability. It is very useful to get icc for many reasons and it is easy to do so from linear mixed-effects models and many packages like psy, psychometric, aod and irr have functions to calculate icc.

icc = between-group variance/(between-group variance + residual variance)

*residual variance = within-group variance

However, I have yet to find a convincing reference or some sort on how to calculate icc from GLMM. I have found below:

icc = between-group variance/(between-group variance + 1)
*between-group variance = scaled between-group variance????
Or variance obtained from random intercept of GLMM icc = between-group variance/(between-group variance + pi^2/3) icc = between-group variance/(between-group variance + pi^2/3*(dispersion parameter))
for binomial GLMM
icc = between-group variance/(between-group variance + 1/(p(1-p))

I am a little confused which one to trust and use. Or there are no easy formulas to do this? I am guessing formula would change depending on what distribution you use and what link function as well? I want to calculate icc from GLMM with Poisson with log link function and also binomial with logit function. Could anybody help me please?

Many thanks for your help

Shinichi

-- 
Shinichi Nakagawa
Dept of Animal & Plant Sciences
University of Sheffield
Tel: 0114-222-0113
Fax: 0114-222-0002

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Received on Fri 08 Jun 2007 - 09:43:34 GMT

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