Bayesian Mediation Analysis with Latent Variables at Small Sample Sizes

3^RD PAPER WITHIN ORGANIZED POSTER FORUM

ABSTRACT BODY: Bayesian methods for structural equation modeling require smaller sample sizes per number of estimated parameters than Maximum Likelihood estimation, and results of a Bayesian analysis can be interpreted in terms of probability (Lee & Song, 2004; Rindskopf, 2012). For these reasons, Bayesian statistics have been becoming more popular in the social sciences, and are often recommended for solving issues in small sample size research (e.g., lack of convergence and low power). Bayesian methods for mediation analysis can have more power than commonly used frequentist methods in manifest variable models, even with diffuse prior distributions. However, with latent variables, Bayesian mediation analysis with diffuse priors can yield worse statistical properties than commonly used frequentist methods (Chen, Choi, Weiss, & Stapleton, 2014), and the pros and cons of using informative priors have yet to be evaluated. This paper will summarize the first examination of using both diffuse and informative (accurate and inaccurate) priors in Bayesian mediation analysis with latent variables at N = 50.

A Monte Carlo study was conducted evaluating the impact of diffuse (noninformative) and informative priors. The informativeness of the prior was selected in a way that makes the prior have one half of the influence relative to the observed sample. The accurate priors for structural paths had mean hyperparameters equal to the true values of the corresponding coefficient. The inaccurate priors for structural paths had mean hyperparameters that were .5, 1, 2, and 3 standard deviations away from the true value of the corresponding parameter.

Findings from a Monte Carlo study suggest that at N = 50 frequentist methods have higher power than Bayesian methods with diffuse priors, and informative priors with even the smallest amount of inaccuracy tested in this study can yield relative bias above 10% for the point summaries of the mediated effect, and reduce power of the interval summaries of the mediated effect by14% or more.

Even though Bayesian methods have been recommended as a way to increase power and avoid convergence issues in SEM with small sample sizes, the findings from this study suggest that the risks of using Bayesian methods with informative priors are very high.