The effect of various simultaneous sources of mechanical error in the estimators of correlation causing defation in reliability: seeking the best options of correlation for defation‑corrected reliability

Abstract

<p>Estimates of reliability by traditional estimators are deflated, because the item-total or item-score correlation (<em>Rit</em>) or principal component or factor loading (<em>λ</em>_<em>i</em>) embedded in the estimators are seriously deflated. Different optional estimators of correlation that can replace <em>Rit</em> and <em>λ</em>_<em>i</em> are compared in this article. Simulations show that estimators such as polychoric correlation (<em>R</em>_<em>PC</em>), gamma (<em>G</em>), dimension-corrected <em>G</em> (<em>G</em>₂), and attenuation-corrected <em>Rit</em> (<em>R</em>_<em>AC</em>) and <em>eta</em> (<em>E</em>_<em>AC</em>) reflect the true correlation without any loss of information with several sources of technical or mechanical error in the estimators of correlation (MEC) including extreme item difficulty and item variance, small number of categories in the item and in the score, and the varying distributions of the latent variable. To obtain deflation-corrected reliability, <em>R</em>_<em>PC</em>, <em>G</em>, <em>G</em>₂, <em>R</em>_<em>AC</em><em>,</em> and <em>E</em>_<em>AC</em> are likely to be the best options closely followed by r-bireg or r-polyreg coefficient (<em>R</em>_<em>REG</em>).<br></p>