This paper reviews many different estimators of intraclass correlation that
have been proposed for binary data and compares them in an extensive simul
ation study. Some of the estimators are very specific, while others result
from general methods such as pseudo-likelihood and extended quasi-likelihoo
d estimation. The simulation study identifies several useful estimators, on
e of which does not seem to have been considered previously for binary data
. Estimators based on extended quasi-likelihood are found to have a substan
tial bias in some circumstances.