Fig. 3

Root mean squared error (RMSE) of β₁ multiplied by the square root of the number of clusters (N) divided by 10 with generalized estimating equations (GEE), single-step augmented GEE (augGEE1), iterated augmented GEE (augGEE), single-step augmented GEE with independent working correlation structure (augGEE1, ind) and penalized GEE (pGEE) for the 36 scenarios. Regression coefficient β₁ corresponds to the binary main variable of interest with a true value of 0.69. In the calculation of the RMSE, non-convergent fits by ordinary GEE, augmented GEE or penalized GEE were replaced by the results from single-step augmented GEE with independent working correlation structure. For scenarios with small, moderate or large cluster size, the numbers of observations per cluster were sampled from a truncated Poisson distribution with mean 5, 10 or 20, respectively. A moderate or large correlation refers to a correlation coefficient of 0.7 or 0.9 at the level of latent responses. ‘Event rate’ denotes the expected proportion of Y = 1 in a scenario