Table 1

Hypothetical data showing that the size of the intraclass correlation (ICC) calculated by the simulation method6 in a multilevel logistic model depends of the prevalence of the outcome (that is, the predicted probability). We present 11 cases, all with the same area variance VA but with different outcome prevalence (pI)

Prevalence pI of the outcome (probability scale)Prevalence of the outcome on the logistic scale (intercept MC)Area variance VA on the logistic scaleArea variance converted to the probability scale*Individual variance**Intraclass correlation ICC = */(*+**)
*To convert the area level variance to the probability scale, we simulated 100000 area level residuals EC–A based on the area level variance VA, and calculated the predicted probability in each of these 100000 simulated area as p = exp (MC+EC-A) /[1+exp (MC+EC-A)]. We computed the area level variance on the probability scale as the variance of these predicted probabilities. **The overall individual level variance is computed as the mean of the individual level variances computed as p (1−p) for each of the 100000 simulated values.
0.01−4.60.20.000030.01080.002 (ie, 0.2%)
0.1−2.20.20.001850.09360.019 (ie, 1.9%)
0.2−1.40.20.005190.15890.032 (ie, 3.2%)
0.3−0.80.20.008720.20790.040 (ie, 4.0%)
0.4−0.40.20.010630.23040.044 (ie, 4.4%)
0.50.00.20.011360.23860.045 (ie, 4.5%)
0.60.40.20.010620.23050.044 (ie, 4.4%)
0.70.80.20.008720.20800.040 (ie, 4.0%)
0.81.40.20.005180.15900.032 (ie, 3.2%)
0.92.20.20.001850.09360.019 (ie, 1.9%)
0.994.60.20.000030.01080.002 (ie, 0.2%)