How Measurement Quality Shapes the Detection of Relationships Between Latent Constructs in Education Sciences: A Monte Carlo Simulation Study

Educational research frequently examines relationships among latent constructs using composite scores or latent-variable models, yet the consequences of measurement quality for structural inference remain insufficiently understood. This study investigated how factor loading, sample size, and population relationship strength influence estimation accuracy and relationship detection using observed-score regression (OSR) and latent-variable structural equation modeling (LV-SEM). A Monte Carlo simulation was conducted using two latent constructs, each represented by six continuous indicators, with sample sizes of 100, 200, 300, and 500, factor loadings of 0.10-0.90, and population regression coefficients of 0.10-0.50. The full factorial design comprised 180 conditions with 1,000 replications per condition. Performance was evaluated using bias, relative bias, RMSE, statistical power, and estimation validity. OSR showed consistent estimation across conditions but substantial attenuation at low factor loadings, with relative bias reaching -94% at a loading of 0.10. LV-SEM substantially reduced attenuation bias at moderate to high loadings, but this advantage did not consistently translate into lower RMSE or higher statistical power. Statistical power increased with sample size, factor loading, and population relationship strength. These findings demonstrate that measurement quality is critical to structural inference and should be considered jointly with sample size, expected relationship strength, and analytical method.