[R-sig-ME] Getting intraclass correlations from a binomial mixed model with logit link

[Ulf Köther]

Dear list members,

I am asking you for help on interpretating the random effects from a
binomial model (strictly 0-1 responses) with a logit link:

Random effects:
 Groups                     Name        Variance Std.Dev.
 ID                         (Intercept) 0.1475   0.3840  
 Item:Emotion               (Intercept) 2.7546   1.6597  
 Emotion                    (Intercept) 0.6822   0.8259  
Number of obs: 4788, groups:  ID, 114; Item:Emotion, 42; Emotion, 7


I would like to get an ICC for each random intercept, but there are some
conceptional problems here I cannot solve yet:

1.) ID and Item are completely crossed random effects, but Items are
nested within Emotion, so I do not know if I just can get an ICC for
each variance component via

sigma-ID^2 / (sigma-ID^2 + sigma-Item:Emotion^2 + sigma-Emotion^2 +
(pi^2/3))

with pi^2/3 as the "residual variance"-equivalent term for a binomial
logit model. The variance parts for the other random intercepts would be
calculated accordingly.

I read the Papers from Goldstein (2002) and Browne (2005) about
partitioning the variance but did not find any concrete hints about such
a model which consists of crossed and nested random effects.

2.) As a side question, I would like to know if one can get these ICCs
(if it is possible to get in the first place) on the probability scale
and not on the logit scale as presented in the model output? I assume
that just applying the inverse link function on the ICC would be no good
idea, but this is just a feeling... Does anyone know, why that is wrong?

Thanks for your help,

kind regards, Ulf

-- 
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Dipl.-Psych. Ulf Köther

PEPP-Team 
Klinik für Psychiatrie und Psychotherapie
Universitätsklinikum Hamburg-Eppendorf
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20246 Hamburg

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Tel.: +49 (0) 40 7410 53248
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Mobil: (9) 55851
ukoether at uke.de
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