Power priors for latent variable mediation models under small sample sizes.

Area of Science:

• Statistics
• Psychometrics
• Biostatistics

Background:

• Latent variable models often need large sample sizes for reliable results.
• Bayesian analysis with small samples benefits from informative priors, particularly power priors using historical data.
• Existing power prior methods are not always suitable for latent variable models.

Purpose of the Study:

• To evaluate two adaptable power prior methods for latent variable models: Mahalanobis weight (MW) and univariate priors.
• To compare their performance against diffuse and weakly informative priors in small sample scenarios.
• To assess convergence, bias, efficiency, and credible interval coverage for indirect effect estimation.

Main Methods:

• Applied MW and univariate power priors, alongside diffuse and weakly informative priors.
• Utilized a latent variable mediation model.
• Simulated various sample sizes and degrees of non-exchangeability.

Main Results:

• Diffuse and univariate priors resulted in poor convergence.
• Weakly informative and MW priors improved convergence and provided reasonable estimates.
• MW priors showed suboptimal performance under certain non-exchangeable conditions.

Conclusions:

• Weakly informative priors offer a reliable approach for latent variable models with small samples.
• The MW prior shows promise but requires further refinement for non-exchangeable data.
• Future research should address limitations of current power prior methods in latent variable analysis.