# Calculating Repeatability by MCMCglmm

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:

prior=list(R=list(V=1,fix=1),G=list(G1=list(V=1,nu=1000,alpha.mu=0,alpha.V=1),G2=list(V=1,nu=1000,alpha.mu=0,alpha.V=1)))

And the model was run with the syntax:

mod<-MCMCglmm(Aggression~1,random=~colony+ID,data=data,family="ordinal",prior=prior,nitt=500000, thin=1000,burnin=50000,verbose=F).

From this, the posterior mode was extracted as follows:

posterior.mode(mod\$VCV).

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!