A New Expression and Interpretation of Coefficient Omega Under the Congeneric One-Factor Model
Publication date
2023-03-18
Authors
Hessen, David
Editors
Ark, L. Andries van der
Emons, Wilco H. M.
Meijer, Rob R.
Advisors
Supervisors
Document Type
Part of book
Metadata
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taverne
Abstract
A new expression for the communality of the total score under the one-factor model is presented. In general, the communality of the total score is a lower bound to the reliability of the total score. Under the one-factor model, the communality of the total score also assesses the validity of the total score as a measure of the common factor. Conditions are given under which the new expression equals coefficient alpha. Furthermore, new expressions for the communality of an arbitrary item score and the proportion of total variance explained are derived under the one-factor model. For all new communality expressions, closed-form distribution-free estimates are provided. In an example, the closed-form estimates are calculated for a classic data set.
Keywords
Coefficient alpha, Coefficient omega, Communality, One-factor model, Reliability, Taverne, Education, Development
Citation
Hessen, D J 2023, A New Expression and Interpretation of Coefficient Omega Under the Congeneric One-Factor Model. in L A V D Ark, W H M Emons & R R Meijer (eds), Methodology of Educational Measurement and Assessment. 1 edn, Methodology of Educational Measurement and Assessment, Springer, Cham, pp. 111-118. https://doi.org/10.1007/978-3-031-10370-4_6