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.