How Many Countries for Multilevel Modeling? A Comparison of Frequentist and Bayesian Approaches

Researchers in comparative research increasingly use multilevel models to test effects of country‐level factors on individual behavior and preferences. However, the asymptotic justification of widely employed estimation strategies presumes large samples and applications in comparative politics routinely involve only a small number of countries. Thus, researchers and reviewers often wonder if these models are applicable at all. In other words, how many countries do we need for multilevel modeling? I present results from a large‐scale Monte Carlo experiment comparing the performance of multilevel models when few countries are available. I find that maximum likelihood estimates and confidence intervals can be severely biased, especially in models including cross‐level interactions. In contrast, the Bayesian approach proves to be far more robust and yields considerably more conservative tests.