ICC from lmer with back transform

Hi,

I am not sure I understand your calculation proposal, but if you want to compute the ICC from the original scale before a log-transformation, you will need to also account for the intercept and the formula is a bit more complex. You can see equations 35 and 36 of:
Nakagawa, S. & Schielzeth, H. Repeatability for Gaussian and non Gaussian data: a practical guide for biologists. Biological Reviews 85, 935?956 (2010).

Note that, due to Jensen's inequality, I believe that, to use these equations, you'd need your to use a log-link rather than a log-transform in the formula (although in practice, the difference might be subtle). Something like:

model <- lmer(VARIABLE ~ 1 +(1|Side)+(1|Asessor)+(1|ID), data = data, family = gaussian(link = "log"), REML=FALSE)

Hope this helps,
Pierre

Le vendredi 30 octobre 2020, 11:08:30 CET fabien leboeuf a ?crit :

Hello
what a nice idea to have a forum dedidated to lmer question :-). i came
acros it from cross-validated.

Here is my question:

I want to calculate the ICC from a mixed model coded with lmer as follow.

model <- lmer(formula = log(VARIABLE) ~ 1
+(1|Side)+(1|Asessor)+(1|ID), data = data,REML=FALSE)

am i wrong if i compute the iCC from back transform , like that

vc <- as.data.frame((VarCorr(model)))
ICC_log = sum(exp(vc$vcov[1]),exp(vc$vcov[3]))/(sum(exp(vc$vcov)))

I appreciate any replies.

Fabien