Effect size for multilevel models
$$\rho = \frac{\mbox{variance(between subjects)}}{\mbox{(variance(between subjects) + variance(within subjects)}}$$
In the wikipedia it states that this "design effect" is used with cluster observations. If we fit a mixed model with a random subject-specific intercept, the clusters are the observations within a participant e. g. the 7 times the participant chose a fruit or a snack. The "design effect" is
D_{eff} = 1 + (m-1) $$\rho$$
where m is the number of observations in each cluster (e.g. number of repeated measures per subject).