Sample Size and Accuracy of Estimates in Multilevel Models. New Simulation Results

In a multilevel framework several researches have investigated the behavior of estimates in finite samples, particularly for continuous dependent variables. Some findings show poor precise estimates for the variance components. On the other hand, discrete response multilevel models have been investigated less widely. In this paper we analyze the influence of different factors on the accuracy of estimates and standard errors of estimates in a binary response 2-level model, through a Monte Carlo simulation study. We investigate the hypothesis of: (a) small sample sizes; (b) different intraclass correlation coefficients; (c) different numbers of quadrature points in the estimation procedure. Standard errors of estimates are studied through a noncoverage indicator. In all instances we have considered, the point estimates are unbiased (even with very small sample sizes), while the variance components are underestimated. The accuracy of the standard errors of variance estimates needs a very large number of groups.