Small Sample Methods in Multilevel Analysis

Abstract

Bayesian methods have been said to solve small sample problems in frequentist methods by reflecting prior knowledge in the prior distribution. However, there are dangers in strongly reflecting prior knowledge or situations where much prior knowledge cannot be used. In order to address the issue, in this article, we considered to apply two Bayesian methods, one with weakly informative prior for random effect parameters (BayesW) and another with non-informative prior (BayesN) and compared their performance of parameter recovery with restricted maximum likelihood (REML) method, a frequentist-based estimation method commonly used in multilevel analysis. Specifically, we conducted two simulation studies using a two-level linear multilevel model and compared the performance of the BayesW, the BayesN, and the REML in various conditions that include scenarios of small sample data with a combination of small sample size both at level-1 and level-2. The results showed that the REML performed better than the BayesW, which showed overall better performance than the BayesN, in terms of convergence, bias, and coverage in some small sample scenarios. Therefore, based on the results of the present study, it is recommended to use the REML when adapting the two-level linear multilevel model and analyzing real-world data with small samples.