Replication data for: 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 justification of widely employed estimation strategies is asymptotic 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.

比较研究领域的研究者日益广泛采用多层模型（multilevel models），以检验国家层面因素对个体行为与偏好的影响效应。然而，当前主流使用的估计策略的合理性依据仅基于渐近理论，而比较政治学中的此类应用通常仅涉及少量国家。因此，研究者与期刊评审者常会质疑这类模型是否真的适用。换言之，开展多层建模究竟需要多少个国家样本？本文呈现了一项大规模蒙特卡洛（Monte Carlo）实验的研究结果，该实验对比了在国家数量有限的情境下多层模型的建模表现。研究发现，极大似然估计值与置信区间可能存在严重偏倚，尤其是在包含跨层交互项的模型中。与之形成鲜明对比的是，贝叶斯（Bayesian）方法展现出更强的稳健性，且能生成更为保守的统计检验结果。