Estimation of Random Coefficient Multilevel Models in the Context of Small Numbers of Level 2 Clusters

• Published in: Educational and psychological measurement Vol. 79; no. 2; pp. 217 - 248
• Main Authors: Bolin, Jocelyn H., Finch, W. Holmes, Stenger, Rachel
• Format: Journal Article
• Language: English
• Published: Los Angeles, CA SAGE Publications 01.04.2019; SAGE PUBLICATIONS, INC
• Subjects: Bayesian analysis; Bayesian Statistics; Computation; Error of Measurement; Hierarchical Linear Modeling; Markov Processes; Maximum Likelihood Statistics; Monte Carlo Methods; Monte Carlo simulation; Parameter estimation; Sample Size; Statistical Analysis; Statistical Bias; multilevel modeling; random coefficients; small samples; fixed effects modeling
• ISSN: 0013-1644; 1552-3888
• DOI: 10.1177/0013164418773494

Multilevel data are a reality for many disciplines. Currently, although multiple options exist for the treatment of multilevel data, most disciplines strictly adhere to one method for multilevel data regardless of the specific research design circumstances. The purpose of this Monte Carlo simulation study is to compare several methods for the treatment of multilevel data specifically when there is random coefficient variation in small samples. The methods being compared are fixed effects modeling (the industry standard in business and managerial sciences), multilevel modeling using restricted maximum likelihood (REML) estimation (the industry standard in the social and behavioral sciences), multilevel modeling using the Kenward–Rogers correction, and Bayesian estimation using Markov Chain Monte Carlo. Results indicate that multilevel modeling does have an advantage over fixed effects modeling when Level 2 slope parameter variance exists. Bayesian estimation of multilevel effects can be advantageous over traditional multilevel modeling using REML, but only when prior probabilities are correctly specified. Results are presented in terms of Type I error, power, parameter estimation bias, empirical parameter estimate standard error, and parameter 95% coverage rates, and recommendations are presented.