[R] icc from GLMM?

[Gregor Gorjanc]

Shinichi Nakagawa <S.Nakagawa <at> sheffield.ac.uk> writes:
... 
> I am a little confused which one to trust and use. Or there are no easy form
> 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?

Yes, you are right that ICC depends on assumed data distribution. While ICC is
very handy in linear models it is not the case in GLMM. I suggest you take a
look at the references bellow. There is also some online material by the same
authors. Additionally, I remember that there were lively discussions about ICC
on "multilevel" list at

http://www.jiscmail.ac.uk/lists/multilevel.html

Best wishes, Gregor

@Article{Goldstein:2002,
  author =       {Goldstein, H. and Browne, W. and Rabash, J.},
  title =        {Partitioning variation in multilevel models},
  journal =      {Understanding Statistics},
  year =         {2002},
  volume =       {1},
  number =       {4},
  pages =        {223--231},
  keywords =     {variance ratio, variance partition coefficient,
                  intra-unit correlation, intra-class correlation, normal
                  models, discrete models, random coefficient models}
}

@Article{Browne:2005,
  author =       {Browne, W. J. and Subramanian, S. V. and Jones, K. and
                  Goldstein, H.},
  title =        {Variance partitioning in multilevel logistic models that
                  exhibit overdispersion},
  journal =      {J. R. Stat. Soc. A Stat. Soc.},
  year =         {2005},
  volume =       {168},
  number =       {3},
  pages =        {599--613},
  doi =          {10.1111/j.1467-985X.2004.00365.x},
  checked =      {[2006-04-16]},
  keywords =     {heritability, ratios, intra-class correlation,
                  intra-unit correlation, simulation, linearization, latent
                  variable approach},
}