A Monte Carlo analysis of multilevel binary logit model estimator performance
Social scientists are increasingly fitting multilevel models to datasets in which a large number of individuals (N ~ several thousands) are nested within each of a small number of countries (C ~ 25). The researchers are particularly interested in â€œcountry effectsâ€ , as summarized by either the coefficients on country-level predictors (or cross-level interactions) or the variance of the country-level random effects. Although questions have been raised about the potentially poor performance of estimators of these â€œcountry effectsâ€ when C is â€œsmallâ€ , this issue appears not to be widely appreciated by many social scientist researchers. Using Monte Carlo analysis, I examine the performance of two estimators of a binary-dependent two-level model using a design in which C = 5(5)50 100 and N = 1000 for each country. The results point to i) the superior performance of adaptive quadrature estimators compared with PQL2 estimators, and ii) poor coverage of estimates of â€œcountry effectsâ€ in models in which C ~ 25, regardless of estimator. The analysis makes extensive use of xtmelogit and simulate and user-written commands such as runmlwin, parmby, and eclplot. Issues associated with having extremely long runtimes are also discussed.
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