I'm wondering what is the strategy to calculate and report the repeatability of multiple measurer in a long term database. I'm rarely seeing people correct or report the values and I was wondering how to do this.

Basically, I imagine that one would want to have the repeatability for a trait that was measured by multiple observer (to know the actual value that the measurer are adding to the animal, I thought putting it as a fixed effect). But this is not repeatability, but the observer effect. In this case, do we look only at the significance of their effect?

mod.out1 = lmer(trait ~ observer + (1|animal.ID), data = database)

After, you could put the observer as a random effect and see how much variance it explains (but I don't get the "observer" effect.)

mod.out2 = lmer(trait ~ 1 + (1|observer) + (1|animal.ID), data = database)

library(sjstats)

icc(mod.out1) # This will report the Intraclass-Correlation Coefficient, but not the actual value for each observer (looking at repeatability per observer).

Then, if there are multiple traits or the same trait that was measured multiple times, is it possible to do this:

mod.out3 = lmer(cbind(trait1, trait2, trait3) ~ 1 + (1|observer) + (1|animal.ID), data = database)

How is it possible to get the repeatability per observer? How to report the repeatability?

There is a specific example here: https://stats.stackexchange.com/questions/412034/how-is-it-possible-to-control-for-observer-bias-in-measurements-with-a-random-ef

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