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

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.

Automated summary

Bayesian approaches are beneficial for estimating multilevel latent variable models in small samples, with prior distributions being used to overcome small sample problems by increasing the accuracy of estimation. This article discusses two approaches for specifying priors that aim at stabilizing estimators to reduce the MSE of the between-group slope estimator. Both approaches, involving slightly informative priors, have been shown to effectively reduce MSE in small samples, making them attractive options in such situations.