Bhirkuti's Relative Efficiency (BRE): Examining its Performance in Psychometric Simulations

Abstract: Traditional Relative Efficiency (RE), based solely on variance, has limitations in evaluating estimator performance, particularly in planned missing data designs. We introduce Bhirkuti's Relative Efficiency (BRE), a novel metric that integrates precision and accuracy to provide a more robust assessment of efficiency. To compute BRE, we use interquartile range (IQR) overlap to measure precision and apply a bias adjustment factor based on the absolute median relative bias (AMRB). Monte Carlo simulations using a Latent Growth Model (LGM) with planned missing data illustrate that BRE maintains theoretically consistency and interpretability, avoiding paradoxes such as RE exceeding 100%. Visualizations via boxplots and ridgeline plots confirm that BRE provides a stable and meaningful estimator efficiency evaluation, making it a valuable advancement in psychometric and statistical modeling. By addressing fundamental weaknesses in traditional RE, BRE provides a superior, theoretically justified alternative for relative efficiency in psychometric modeling, structural equation modeling, and missing data research. This advancement enhances data-driven decision-making and offers a methodologically rigorous tool for researchers analyzing incomplete datasets.