Sufficient Sample Sizes for Multilevel Modeling

TLDR

An important problem in multilevel modeling is determining what constitutes a sufficient sample size for accurate estimation, with the higher-level sample size often being the major restriction. This paper uses a simulation study to assess how different group-level sample sizes affect the accuracy of regression coefficients, variance components, and their standard errors. The study also examines the impact of lowest-level sample size and varying intraclass correlations across levels. Results show that a level‑two sample size of 50 or fewer biases second‑level standard errors, while larger samples yield unbiased estimates of coefficients, variances, and standard errors. Abstract.

Abstract

Abstract. An important problem in multilevel modeling is what constitutes a sufficient sample size for accurate estimation. In multilevel analysis, the major restriction is often the higher-level sample size. In this paper, a simulation study is used to determine the influence of different sample sizes at the group level on the accuracy of the estimates (regression coefficients and variances) and their standard errors. In addition, the influence of other factors, such as the lowest-level sample size and different variance distributions between the levels (different intraclass correlations), is examined. The results show that only a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second-level standard errors. In all of the other simulated conditions the estimates of the regression coefficients, the variance components, and the standard errors are unbiased and accurate.