I am conducting latent measurement invariance analyses using MPlus. The data are best modeled by a single factor (A) and a reverse-coded method factor (RC). All six items load onto A; three of the six items load onto RC.
I would like to calculate composite reliability (omega) for A. It appears that the variance of the dual-loading items is affected (lowered) by this factor structure, which results in potentially liberal estimations of omega. Modeling the data using a correlated error structure provides markedly higher variances for the cross loading items, and, thus, a lower estimation for omega.
What is the appropriate way to calculate omega for data with this structure? Thank you very much for your help,
Chris Napolitano
Christopher,
here are some other articles that may also be helpful:
Rodriguez, A., Reise, S. P., & Haviland, M. G. (2015, November 2). Evaluating Bifactor Models: Calculating and Interpreting Statistical Indices. Psychological Methods. Advance online publication. http://dx.doi.org/10.1037/met0000045
Abstract: Bifactor measurement models are increasingly being applied to personality and psychopathology measures (Reise, 2012). In this work, authors generally have emphasized model fit, and their typical conclusion is that a bifactor model provides a superior fit relative to alternative subordinate models. Often unexplored, however, are important statistical indices that can substantially improve the psychometric analysis of a measure. We provide a review of the particularly valuable statistical indices one can derive from bifactor models. They include omega reliability coefficients, factor determinacy, construct reliability, explained common variance, and percentage of uncontaminated correlations. We describe how these indices can be calculated and used to inform: (a) the quality of unit-weighted total and subscale score composites, as well as factor score estimates, and (b) the specification and quality of a measurement model in structural equation modeling.
Tenko Raykov & George A. Marcoulides (2016) Scale Reliability Evaluation
Under Multiple Assumption Violations, Structural Equation Modeling: A Multidisciplinary Journal, 23:2, 302-313, DOI: 10.1080/10705511.2014.938597
Abstract: A latent variable modeling approach to evaluate scale reliability under realistic conditions in empirical behavioral and social research is discussed. The method provides point and interval estimation of reliability of multicomponent measuring instruments when several assumptions are violated. These assumptions include missing data, correlated errors, nonnormality, lack of unidimensionality, and data not missing at random. The procedure can be readily used to aid scale construction and development efforts in applied settings, and is illustrated using data from an educational study.
HTH
Karin
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