Evaluation of the Bayesian and Maximum Likelihood Approaches in Analyzing Structural Equation Models with Small...

Area of Science:

• * Statistics
• * Quantitative Psychology
• * Econometrics

Background:

• * Structural Equation Models (SEM) are widely used in various scientific disciplines.
• * Analyzing SEM with small sample sizes presents challenges for traditional methods.
• * Maximum Likelihood (ML) is a common estimation method, but its performance can degrade with limited data.

Purpose of the Study:

• * To empirically evaluate the performance of the Bayesian approach in SEM with small sample sizes.
• * To compare the Bayesian approach against the traditional Maximum Likelihood (ML) method.
• * To assess the accuracy of parameter estimates and goodness-of-fit statistics under small sample conditions.

Main Methods:

• * Simulation studies were conducted using confirmatory factor analysis and SEM.
• * Sample sizes were varied (n = da, where d = 2, 3, 4, 5 and 'a' is the number of parameters).
• * Performance was assessed using goodness-of-fit indices and accuracy measures for parameter estimates.

Main Results:

• * The Bayesian approach demonstrated robust performance in analyzing SEM with small sample sizes.
• * Maximum Likelihood (ML) estimation showed significant limitations and inaccuracies under small sample conditions.
• * The Bayesian method provided more reliable parameter estimates and goodness-of-fit statistics when data were normally distributed.

Conclusions:

• * The Bayesian approach is a viable and recommended method for SEM analysis when dealing with small sample sizes, particularly for normally distributed data.
• * Researchers should consider the Bayesian approach over ML for small sample SEM to ensure accurate and reliable results.
• * This study provides empirical evidence supporting the use of Bayesian methods in data-limited research scenarios.