I am analysing repeatabilities of behavioural traits. One of the behaviours appeared to be affected by the "repeat number". I need to calculate the adjusted repeatability, but after reading papers I still have no idea how. Is there anybody who could describe me the procedure in a very simple way. Thanks a lot!!!
Hi Simona,
This can easily be done in the package lme4 with a mixed model approach. You'd just have to add the "repeat number" as a fixed effect in your model, + any other covariate that may influence behavior (temperature, body size etc).
Here's how that would work code wise:
library(lme4)
LMM=lmer(behavior~repeat_nb+...+(1|Id), data = yourdata)
summary(LMM);confint(LMM)
The summary function then returns the variance for the random effects with which you can calculate repeatability. Confint will return confidence intervals for both random and fixed effects.
Hope this helps!
Raphael is correct. There's a nice discussion of the mixed model approach in the "Controlling for Counfounding Factors" section of Nakagawa and Schielzeth's 2010 paper (doi: 10.1111/j.1469-185X.2010.00141). They also refer to a couple of papers that have applied the measure in various ways. Forgive me if you've already read it, but it might help.
Thank you very much for that. Now I am not sure if this is applicable for count data (dependent variable)?
This is what I got:
> summary(LMM)
Linear mixed model fit by REML ['lmerMod']
Formula: For ~ repeat. + age + (1 | ID)
Data: K
REML criterion at convergence: 422.9
Scaled residuals:
Min 1Q Median 3Q Max
-1.98112 -0.72262 -0.03266 0.73123 2.27608
Random effects:
Groups Name Variance Std.Dev.
ID (Intercept) 0.1963 0.4431
Residual 0.6754 0.8218
Number of obs: 154, groups: ID, 71
Fixed effects:
Estimate Std. Error t value
(Intercept) 0.471980 0.330782 1.427
repeat. 0.431539 0.107667 4.008
age 0.001181 0.005836 0.202
Correlation of Fixed Effects:
(Intr) repet.
repeat. -0.963
age 0.810 -0.791
> confint(LMM)
Computing profile confidence intervals ...
2.5 % 97.5 %
.sig01 0.13172583 0.6405711
.sigma 0.70764854 0.9557547
(Intercept) -0.18016888 1.1185339
repeat. 0.22112358 0.6446632
age -0.01021063 0.0125706
Is it correct R=0.19 / (0.19 + 0.675)=0.22 ?
I do not get what is CI now...0.22 - 0.644???
Thanks!
Hi Simona,
1) Repeatability calculation. Correct! For the CI of the random effects, I forgot to mention that those are calculated on the standard deviation and not the variance by default. So the CI for repeatability becomes: lower CI = 0.13172583^2/(0.13172583^2+0.70764854^2) = 0.03; upper CI = 0.6405711^2/(0.6405711^2+0.9557547^2) = 0.31.
2) Count data. You basically have 2 solutions here.
- If the range of possible values for your behaviors is large (say For varies between 0 and 50) and if this variable looks relatively normally distributed you may not have to change anything (hist(K$For)). Using a square-root transformation may also help. You should also check the normality of your residuals: hist(residuals(LMM)).
- If the your range of values is narrow (say 15-20 possible values or lower), then you should use a GLMM with Poisson distribution. However, the repeatability has to be calculated a little differently because of that (following Nakagawa and Schielzeth 2010 paper). The easiest way to do that in lme4 would be:
obs
Raphael,
thank you, that was really helpful...though unfortunately adj R is now 0 (CI=0, 0.58)...
Yeah, that can happen when there is too little information for the model to properly estimate the random effect components (i.e. not enough measures per individuals).
Again, if the residuals from your gaussian mixed model don't depart too much from a normal distribution, your first estimate should be fine. You could try a Bayesian mixed model to see if it also returns a repeatability of 0, but that becomes much more complex in terms of coding.
Thanks a lot Petri for your help! I know I was avoiding R for too long....
Repeatability is still close to zero...but results seem to be solid now.
Cheers,
Simona
you can estimate repeatability by rptR packages in R. at first you must deside about gaussian or non Gaussian data
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