Estimation of Path Coefficient Parameter Based on The Best RMSEA Value in Structural Equation Modeling Weighted Least Square

Abstract

Structural Equation Modeling (SEM) is a statistical approach widely used to analyze causal relationships between latent and observed variables. A key issue in SEM lies in selecting an appropriate parameter estimation method, as it strongly affects the accuracy and interpretation of results. Among the most common estimation techniques are Maximum Likelihood (ML) and Weighted Least Squares (WLS). This study aims to compare the performance of ML and WLS in estimating path coefficients within SEM analysis. Using simulated data generated with the simulateData() function from a predefined structural model, three scenarios are examined with sample sizes of 500 and 1000. Data transformation procedures are applied to ensure consistency before model testing. Each SEM model is then estimated using both ML and WLS, and the results are evaluated through Root Mean Square Error of Approximation (RMSEA) values obtained from 100 replications. Findings indicate that WLS generally outperforms ML in terms of model fit and stability. In the first scenario with a sample size of 500, WLS achieves a lower average RMSEA (0.0141) compared to ML (0.0172). With a sample size of 1000 in the second scenario, both methods produce similar RMSEA values (0.009 for WLS and 0.0096 for ML), though WLS demonstrates lower variability. In the third scenario, also with a sample size of 1000, WLS records an average RMSEA of 0.0074 versus 0.0092 for ML. Overall, the results suggest that WLS is more effective and reliable than ML in providing accurate parameter estimates across different data conditions and sample sizes.