Bayesian Versus Frequentist Estimation for Structural Equation Models in Small Sample Contexts: A Systematic Review

Abstract

In small sample contexts, Bayesian estimation is often suggested as a viable alternative to frequentist estimation, such as maximum likelihood estimation. Our systematic literature review is the first study aggregating information from numerous simulation studies to present an overview of the performance of Bayesian and frequentist estimation for structural equation models with small sample sizes. We conclude that with small samples, the use of Bayesian estimation with diffuse default priors can result in severely biased estimatesthe levels of bias are often even higher than when frequentist methods are used. This bias can only be decreased by incorporating prior information. We therefore recommend against naively using Bayesian estimation when samples are small, and encourage researchers to make well-considered decisions about all priors. For this purpose, we provide recommendations on how to construct thoughtful priors.

Predicting a Distal Outcome Variable From a Latent Growth Model: ML versus Bayesian Estimation

“…However, we decided to implement this prior in the current study based on findings of previous studies. Based on a systematic literature review, Smid et al (2019) indicated that informative priors for other parameters in the model could improve the estimates of variance parameters, when default priors were specified for the variance parameters. Depaoli (2012), Depaoli and Clifton (2015), and Holtmann et al (2016) reported similar findings: priors on parameters in one part of the model impacted results for parameters in another part of the model.…”

“…These features are especially valuable under instances of small sample sizes. As discussed inamong many others - Gelman et al (2014) and McNeish (2016a) and echoed in the literature review of Smid, McNeish, Miočević, and van de Schoot (2019), the successful use of Bayesian estimation with small samples requires a thoughtful specification of priors.…”

Small Sample Size Solutions

“…Since we know that at least some degree of information is necessary to properly estimate small data (Smid, McNeish, Miočević, & Van de Schoot, 2019), the next question is: How to assess and use such information? There are many ways to specify subjective priors-for example, based on expert elicitation or previous data (Van de Schoot et al, 2018)-and none are inherently right or wrong.…”

“…Still, some research questions can only be answered with complex statistical models. Fortunately, solutions exist to overcome estimation issues with small sample sizes for complex models; see Smid, McNeish, Miočević, and Van de Schoot (2019) for a systematic review comparing frequentist and Bayesian approaches. The current chapter addresses one of these solutions, namely Bayesian estimation with informative priors.…”

The Moderating Effects of Self-efficacy in the Relationship between Basic Psychological Needs on Smartphone Use and Smartphone Addiction in Adolescents

“…The non-informative priors are generally adequate for the models discuss here as long as the sample size is not small. If the sample size is small, fine-tuning of the priors along the lines of Smid et al (2020) can be beneficial. The simulation study results for the interaction effects are presented in Table 1.…”