| Omega {fungible} | R Documentation |
Compute Omega hierarchical
Description
This function computes McDonald's Omega hierarchical to determine the proportions of variance (for a given test) associated with the latent factors and with the general factor.
Usage
Omega(lambda, genFac = 1, digits = NULL)
Arguments
lambda |
(Matrix) A factor pattern matrix to be analyzed. |
genFac |
(Scalar, Vector) Which column(s) contains the general factor(s). The default value is the first column. |
digits |
(Scalar) The number of digits to round all output to. |
Details
-
Omega Hierarchical: For a reader-friendly description (with some examples), see the Rodriguez et al., (2016) Psychological Methods article. Most of the relevant equations and descriptions are found on page 141.
Value
-
omegaTotal: (Scalar) The total reliability of the latent, common factors for the given test.
-
omegaGeneral: (Scalar) The proportion of total variance that is accounted for by the general factor(s).
Author(s)
Casey Giordano (Giord023@umn.edu)
Niels G. Waller (nwaller@umn.edu)
References
McDonald, R. P. (1999). Test theory: A unified approach. Mahwah, NJ:Erlbaum.
Rodriguez, A., Reise, S. P., & Haviland, M. G. (2016). Evaluating bifactor models: Calculating and interpreting statistical indices. Psychological Methods, 21(2), 137.
Zinbarg, R.E., Revelle, W., Yovel, I., & Li. W. (2005). Cronbach's Alpha, Revelle's Beta, McDonald's Omega: Their relations with each and two alternative conceptualizations of reliability. Psychometrika. 70, 123-133. https://personality-project.org/revelle/publications/zinbarg.revelle.pmet.05.pdf
Examples
## Create a bifactor structure
bifactor <- matrix(c(.21, .49, .00, .00,
.12, .28, .00, .00,
.17, .38, .00, .00,
.23, .00, .34, .00,
.34, .00, .52, .00,
.22, .00, .34, .00,
.41, .00, .00, .42,
.46, .00, .00, .47,
.48, .00, .00, .49),
nrow = 9, ncol = 4, byrow = TRUE)
## Compute Omega
Out1 <- Omega(lambda = bifactor)