fungible (version 2.2.2)

Omega: 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)

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).

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.

Author

• Casey Giordano ([e-mail])

• Niels G. Waller ([e-mail])

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.

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)