Evaluating the Discrepancy Between Scale Reliability and Cronbach’s Coefficient Alpha Using Latent Variable Modeling

References

• Apostol, T. (2013). Calculus. Wiley.
   Google Scholar
• Bollen, K. A. (1980). Issues in the comparative measurement of political democracy. American Sociological Review, 45(3), 370–390. https://doi.org/10.2307/2095172
   Web of Science ®Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. Wiley.
   Google Scholar
• Casella, G., & Berger, J. O. (2002). Statistical inference. Wadsworth.
   Google Scholar
• Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334. https://doi.org/10.1007/BF02310555
   Web of Science ®Google Scholar
• Efron, B., & Tibshiriani, R. J. (1993). An introduction to the bootstrap. CRC Press.
   Google Scholar
• Green, S. B., & Hershberger, S. L. (2000). Correlated errors in true score models and their effect on coefficient alpha. Structural Equation Modeling: A Multidisciplinary Journal, 7(2), 251–270. https://doi.org/10.1207/S15328007SEM0702_6
   Web of Science ®Google Scholar
• McDonald, R. P. (1999). Test theory. A unified treatment. Erlbaum.
   Google Scholar
• McNeish, D. (2018). Thanks coefficient alpha, we’ll take it from here. Psychological Methods, 23(3), 412–433. https://doi.org/10.1037/met0000144
   PubMed Web of Science ®Google Scholar
• Mulaik, S. A. (2009). Foundations of factor analysis. CRC Press.
   Google Scholar
• Muthén, B. O. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29(1), 87–117. https://doi.org/10.2333/bhmk.29.81
   Google Scholar
• Muthén, L. K., & Muthén, B. O. (2021). Mplus user’s guide. Muthén & Muthén.
   Google Scholar
• Novick, M. R., & Lewis, C. (1967). Coefficient alpha and the reliability of composite measurement. Psychometrika, 32(1), 1–13. https://doi.org/10.1007/BF02289400
   PubMed Web of Science ®Google Scholar
• Raykov, T. (1997). Scale reliability, Cronbach’s coefficient alpha, and violations of essential tau-equivalence for fixed congeneric components. Multivariate Behavioral Research, 32(4), 329–354. https://doi.org/10.1207/s15327906mbr3204_2
   PubMed Web of Science ®Google Scholar
• Raykov, T. (2001). Bias of coefficient alpha for congeneric measures with correlated errors. Applied Psychological Measurement, 25(1), 69–76. https://doi.org/10.1177/01466216010251005
   Web of Science ®Google Scholar
• Raykov, T. (2012). Scale development using structural equation modeling. In R. Hoyle (Ed.), Handbook of structural equation modeling (pp. 472–492). Guilford Press.
   Google Scholar
• Raykov, T., & Bluemke, M. (2021). Examining multidimensional measuring instruments for proximity to unidimensional structure using latent variable modeling. Educational and Psychological Measurement, 81(2), 319–339. https://doi.org/10.1177/0013164420940764
   PubMed Web of Science ®Google Scholar
• Raykov, T., Goldammer, P., Marcoulides, G. A., Li, T., & Menold, N. (2018). Reliability of scales with second-order structure: Evaluation of coefficient alpha’s population slippage using latent variable modeling. Educational and Psychological Measurement, 78(6), 1123–1135. https://doi.org/10.1177/0013164417719948
   PubMed Web of Science ®Google Scholar
• Raykov, T., & Marcoulides, G. A. (2004). Using the delta method for approximate interval estimation of parametric functions in covariance structure models. Structural Equation Modeling, 11(4), 659–675. https://doi.org/10.1207/s15328007sem1104_7
   Web of Science ®Google Scholar
• Raykov, T., & Marcoulides, G. A. (2011). Introduction to psychometric theory. New York: Taylor & Francis.
   Google Scholar
• Raykov, T., & Marcoulides, G. A. (2015). Scale reliability evaluation with heterogeneous populations. Educational and Psychological Measurement, 75(5), 875–892. https://doi.org/10.1177/0013164414558587
   PubMedGoogle Scholar
• Raykov, T., & Marcoulides, G. A. (2016). Scale reliability estimation under multiple assumption violations. Structural Equation Modeling: A Multidisciplinary Journal, 23(2), 302–313. https://doi.org/10.1080/10705511.2014.938597
   Web of Science ®Google Scholar
• Raykov, T., & Marcoulides, G. A. (2018). A course in item response theory and modeling with Stata. Stata Press.
   Google Scholar
• Raykov, T., & Marcoulides, G. A. (2019). Thanks Coefficient alpha, we still need you! Educational and Psychological Measurement, 79(1), 200–210. https://doi.org/10.1177/0013164417725127
   PubMed Web of Science ®Google Scholar
• Raykov, T., Marcoulides, G. A., & Chang, C. (2016). Examining population heterogeneity in finite mixture settings using latent variable modeling. Structural Equation Modeling: A Multidisciplinary Journal, 23(5), 726–730. https://doi.org/10.1080/10705511.2015.1103193
   Web of Science ®Google Scholar
• Raykov, T., & Shrout, P. (2002). A method of reliability estimation for composites with general structure. Structural Equation Modeling, 9, 225–236.
   Web of Science ®Google Scholar
• Raykov, T., West, B. T., & Traynor, A. (2015). Evaluation of coefficient alpha for multiple component measuring instruments in complex sample designs. Structural Equation Modeling, 22(3), 429–438. https://doi.org/10.1080/10705511.2014.936081
   Web of Science ®Google Scholar
• Rhemtulla, M., Brosseau-Liard, P., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 18, 354–369. https://doi.org/10.1037/a0029315
   Google Scholar
• Savalei, V., & Reise, S. P. (2019). Don’t forget the model in your model-based reliability coefficients: A reply to McNeish (2018). Collabra: Psychology, 5, 1–8.
   Google Scholar
• Sijtsma, K. (2009). On the use, the misuse, and the very limited usefulness of Cronbach’s Alpha. Psychometrika, 74(1), 107–120. https://doi.org/10.1007/s11336-008-9101-0
   PubMed Web of Science ®Google Scholar
• Widhiarso, W., & Ravand, H. (2014). Examining reliability coefficients for multidimensional measures: A pedagogical illustration. Review of Psychology, 21, 111–121.
   Google Scholar
• Yang, Y., & Green, S. (2011). Coefficient alpha: A reliability coefficient for the 21st century? Journal of Psychoeducational Assessment, 29(4), 377–392. https://doi.org/10.1177/0734282911406668
   Web of Science ®Google Scholar