Prior Specification for More Stable Bayesian Estimation of Multilevel Latent Variable Models in Small Samples: A Comparative Investigation of Two Different Approaches

Steffen Zitzmann; Christoph Helm; Martin Hecht

doi:10.3389/fpsyg.2020.611267

Prior Specification for More Stable Bayesian Estimation of Multilevel Latent Variable Models in Small Samples: A Comparative Investigation of Two Different Approaches

Front Psychol. 2021 Jan 25:11:611267. doi: 10.3389/fpsyg.2020.611267. eCollection 2020.

Authors

Steffen Zitzmann¹, Christoph Helm², Martin Hecht³

Affiliations

¹ Hector Research Institute of Education Sciences and Psychology, University of Tübingen, Tübingen, Germany.
² Institute for the Management and Economics of Education, University of Teacher Education Zug, Zug, Switzerland.
³ Department of Psychology, Humboldt-Universität zu Berlin, Berlin, Germany.

Abstract

Bayesian approaches for estimating multilevel latent variable models can be beneficial in small samples. Prior distributions can be used to overcome small sample problems, for example, when priors that increase the accuracy of estimation are chosen. This article discusses two different but not mutually exclusive approaches for specifying priors. Both approaches aim at stabilizing estimators in such a way that the Mean Squared Error (MSE) of the estimator of the between-group slope will be small. In the first approach, the MSE is decreased by specifying a slightly informative prior for the group-level variance of the predictor variable, whereas in the second approach, the decrease is achieved directly by using a slightly informative prior for the slope. Mathematical and graphical inspections suggest that both approaches can be effective for reducing the MSE in small samples, thus rendering them attractive in these situations. The article also discusses how these approaches can be implemented in Mplus.

Keywords: Bayesian estimation; Markov chain Monte Carlo; multilevel modeling; small sample; structural equation modeling.