The Bayesian unidimensional reliability analysis allows the user to test the scale's ability to consistently measure a unidimensional construct. In other words the analysis indicates the amount of error captured in the measurement.
The CTT-coefficients alpha, lambda 2, lambda 6, and the glb are computed from the data covariance matrix. Coefficient omega is computed from the centered data matrix.
Display the posterior densities of the reliability coeffcients - Fix range to 0-1: fix the x-axis of the plot to the interval [0, 1] - Display priors: display the prior distributions of the coefficients
Since sampling from the posterior distribution is subjected to random processes, one can set a seed so that the background calculations in R yield equal results for equal seeds
The prior distributions for alpha, lambda2, lambda6, the glb, and the average inter-item correlation are induced by the prior distribution on the covariance matrix, which, by default, is an inverse Wishart distribution with the identity matrix as a scaling matrix and the number of items k as the degrees of freedom.
The prior distribution on McDonald’s omega is induced by the prior distributions on the single-factor model parameters, which are: a normal distribution centered on zero for the factor loadings and scores; an inverse gamma distribution with shape=2 and scale=1 for the residuals; and for the variance of the latent variables an inverse Wishart distribution with the number of items k as a scaling matrix (scalar, since it is of dimension one) and k+2 as the degrees of freedom.
This allows the user to select reverse-scaled items that need to be recoded.
Carl F. Falk & Victoria Savalei (2011) The relationship between unstandardized and standardized alpha, true reliability, and the underlying measurement model, Journal of Personality Assessment, 93(5), 445-453. https://doi.org/10.1080/00223891.2011.594129
Hayashi, K. and Kamata, A. 2005. A note on the estimator of the alpha coefficient for standardized variables under normality. Psychometrika, 70, 579–586.
Sun, W., Chou, C. P., Stacy, A. W., Ma, H., Unger, J. and Gallaher, P. 2007. SAS and SPSS macros to calculate standardized Cronbach's alpha using the upper bound of the phi coefficient for dichotomous items. Behavior Research Methods, 39, 71–81.
Moss, J. (2020). Please avoid the standardized alpha and the ordinal alpha. https://doi.org/10.31234/osf.io/nvg5d
Warrens, M.J. Some relationships between Cronbach’s alpha and the Spearman-Brown formula. Journal of Classification, 32, 127–137 (2015). https://doi.org/10.1007/s00357-015-9168-0
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% credible intervalGo to: Open
--> Data Library
--> 13. Reliability
--> ASRM - Mania Scale
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