Which method delivers greater signal-to-noise ratio: Structural equation modelling or regression analysis with...

Area of Science:

• Statistics
• Econometrics
• Psychometrics
• Social Sciences Research Methods

Background:

• Observational data frequently contain measurement errors, impacting statistical analyses.
• Covariance-based structural equation modeling (CB-SEM) can model measurement errors but may not be optimal for prediction.
• Regression analysis with weighted composites is often used for prediction but can yield attenuated coefficients with erroneous predictors.

Purpose of the Study:

• To challenge the conventional view that CB-SEM is superior for analyzing observational data with measurement errors.
• To demonstrate that regression analysis via weighted composites can yield more efficient parameter estimates and a higher signal-to-noise ratio (SNR).
• To compare the performance of least squares (LS) regression with weighted composites against CB-SEM under various conditions.

Main Methods:

• Mathematical derivations comparing the SNR of LS regression with weighted composites and CB-SEM.
• Numerical simulations to evaluate performance under different data conditions.
• Empirical data analysis to validate theoretical findings.

Main Results:

• LS regression using equally weighted composites yields a mathematically greater SNR than CB-SEM when predictor items are parallel, even with correct model specification.
• LS regression with weighted composites performs comparably to or better than normal maximum likelihood for CB-SEM in many scenarios, including multivariate normal distributions.
• Considering sampling errors in composite weights further enhances the efficiency of LS regression coefficients.

Conclusions:

• Regression analysis via weighted composites, particularly using the LS method, is a highly effective approach for analyzing observational data with measurement errors.
• This method offers advantages in parameter estimation efficiency and SNR compared to CB-SEM, contrary to common assumptions.
• The findings suggest a re-evaluation of standard practices favoring CB-SEM for all observational data analyses, especially when prediction is a goal.