Typology of Deflation-Corrected Estimators of Reliability - Metsämuuronen, Jari (Frontiers in Psychology, 2022)
Reliability of a test score is discussed from the viewpoint of underestimation of and, specifically, deflation in the estimates or reliability. Many widely used estimators are known to underestimate reliability. Empirical cases have shown that estimates by the widely used estimators such as alpha, theta, omega, and rho may be deflated up to 0.60 units, or even more, of reliability with certain types of datasets. The reason for this radical deflation lies in the item–score correlation (Rit) embedded in these estimators: because the estimates by Rit are deflated when the number of categories in scales are far from each other, as is the case always with item and score, estimates of reliability are deflated as well. A short-cut method to reach estimates closer the true magnitude, new types of estimators, deflation-corrected estimators of reliability (DCER) are studied in the article. The empirical section is a study of the characteristics of combinations of DCERs formed by different bases for the estimators (alpha, theta, omega, and rho), different alternative estimators of correlation as the linking factor between item and the score variable, and different conditions. Based on a simulation, an initial typology of the families of DCERs is presented: some estimators are better with binary items and some with polytomous items; some are better with small sample sizes and some with larger ones.