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.
This project examined the performance of classical and Bayesian estimators of four effect size measures for the indirect effect in a single-mediator model and a two-mediator model. Compared to the proportion and ratio mediation effect sizes, standardized mediation effect-size measures were relatively unbiased and efficient in the single-mediator model and the two-mediator model. Percentile and bias-corrected bootstrap interval estimates of ab/s Y, and ab(s X)/s Y in the single-mediator model outperformed interval estimates of the proportion and ratio effect sizes in terms of power, Type I error rate, coverage, imbalance, and interval width. For the two-mediator model, standardized effect-size measures were superior to the proportion and ratio effect-size measures. Furthermore, it was found that Bayesian point and interval summaries of posterior distributions of standardized effect-size measures reduced excessive relative bias for certain parameter combinations. The standardized effect-size measures are the best effect-size measures for quantifying mediated effects.
This randomized prospective trial aimed to assess the feasibility and efficacy of a team-based worksite health and safety intervention for law enforcement personnel. Four-hundred and eight subjects were enrolled and half were randomized to meet for weekly, peer-led sessions delivered from a scripted team-based health and safety curriculum. Curriculum addressed: exercise, nutrition, stress, sleep, body weight, injury, and other unhealthy lifestyle behaviors such as smoking and heavy alcohol use. Health and safety questionnaires administered before and after the intervention found significant improvements for increased fruit and vegetable consumption, overall healthy eating, increased sleep quantity and sleep quality, and reduced personal stress.
It was suggested that Bayesian methods have potential for increasing power in mediation analysis (Koopman, Howe, Hollenbeck, & Sin, 2015; Yuan & MacKinnon, 2009). This paper compares the power of Bayesian credibility intervals for the mediated effect to the power of normal theory, distribution of the product, percentile, and bias-corrected bootstrap confidence intervals at N≤ 200. Bayesian methods with diffuse priors have power comparable to the distribution of the product and bootstrap methods, and Bayesian methods with informative priors had the most power. Varying degrees of precision of prior distributions were also examined. Increased precision led to greater power only when N≥ 100 and the effects were small, N < 60 and the effects were large, and N < 200 and the effects were medium. An empirical example from psychology illustrated a Bayesian analysis of the single mediator model from prior selection to interpreting results.
Background Causal inference continues to be a critical aspect of evaluation research. Recent research in causal inference for statistical mediation has focused on addressing the sequential ignorability assumption; specifically, that there is no confounding between the mediator and the outcome variable. Objectives This article compares and contrasts three different methods for assessing sensitivity to confounding and describes the graphical depiction of these methods. Design Two types of data were used to fully examine the plots for sensitivity analysis. The first type was generated data from a single mediator model with a confounder influencing both the mediator and the outcome variable. The second was data from an actual intervention study. With both types of data, situations are examined where confounding has a large effect and a small effect. Subjects The nonsimulated data were from a large intervention study to decrease intentions to use steroids among high school football players. We demonstrate one situation where confounding is likely and another situation where confounding is unlikely. Conclusions We discuss how these methods could be implemented in future mediation studies as well as the limitations and future directions for these methods.
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