I'm trying to calculate repeatability of aggression (ordinal scores ranging from 1 to 6) of individuals. Individuals (ID) are not independent, but are nested within colonies. We know that colonies differ from one another in their aggression levels. Therefore, I would like to include colony as random effects in the model and estimate repeatability in aggression of individuals.
My data consists of 204 individuals from 7 colonies, repeatedly tested for aggression for 4 times. Colonies and individuals (ID) were converted as factors (7 levels and 204 levels respectively) before running the MCMCglmm with family = "ordinal".
The following prior was set:
And the model was run with the syntax:
From this, the posterior mode was extracted as follows:
The output was as follows:
colony: 0.2397765; ID:0.2900612; units: 0.9998443
The repeatability of individuals was calculated as follows:
Repeatability (R) = 0.290/(0.239+0.290+0.999+1), which I guess is equal to between individual variance/total variance. 1 is added to the denominator to account for the probit distribution.
I'm wondering if this is the correct formula for estimating repeatability? Because I get low and unexpected values of repeatability (0.11). Attached below is the trace plot.
Autocorrelation was <0.1. Effective sample sizes were between 360 and 450. Also, the trace plot for colony looks a little wierd?
Any help is much appreciated. Thanks!