Deflation-Corrected Estimators of Reliability

Abstract

Underestimation of reliability is discussed from the viewpoint of deflation in estimates of reliability caused by artificial systematic technical or mechanical error in the estimates of correlation (MEC). Most traditional estimators of reliability embed product–moment correlation coefficient (PMC) in the form of item–score correlation (Rit) or principal component or factor loading (λi). PMC is known to be severely affected by several sources of deflation such as the difficulty level of the item and discrepancy of the scales of the variables of interest and, hence, the estimates by Rit and λi are always deflated in the settings related to estimating reliability. As a short-cut to deflation-corrected estimators of reliability, this article suggests a procedure where Rit and λi in the estimators of reliability are replaced by alternative estimators of correlation that are less deflated. These estimators are called deflation-corrected estimators of reliability (DCER). Several families of DCERs are proposed and their behavior is studied by using polychoric correlation coefficient, Goodman–Kruskal gamma, and Somers delta as examples of MEC-corrected coefficients of correlation.