*! version 1.1 September 8, 2021
help omegacoef

Title

omegacoef -- Calculates McDonald's omega, also known as
Raykov's rho, as a desirable reliability estimate for congeneric scales
comprised of continuous variables.

Syntax

omegacoef varlist [, options]

options

iterate(#) number of iterations; default is 1000

usemissing Consider cases with missing values; recommended when data are missing at random

reverse(varlist) variables that are reverse coded

noreverse(varlist) variables that should not be treated as reverse coded

Description

omegacoef calculates the scale reliability coefficient known as McDonald's
omega (McDonald, 1999), which is also known as Raykov's rho (Raykov, 1997).
Omega is similar to the well-known Cronbach's alpha, but is preferable in almost
all practical applications because Cronbach's alpha has very restricve
assumptions that are rarely met in practice (Hayes and Coutts, 2020; McNeish,
2018). Cronbach's alpha can be regarded as a special case of McDonald's omega
and the two measures will be equivalent when the assumptions for Cronbach's
alpha are met. omegacoef is based on loadings from confirmatory factor
analysis, and is estimated using maximum likelihood. It requires at least three
continuous variables that are all presumed to measure the same construct. The
estimated reliability is often close to Cronbach's alpha, but has been shown to
differ under certain conditions (see McNeish, 2018).

Options

iterate(#) specifies the number of iterations the confirmatory factor
analysis model will use to attempt to converge. In most applications, the model
should converge with just a few iterations. If it does not converge after the
default 1000 iterations it is most likely a sign that there is a specification
issue, which is often the inclusion of a categorical variable. It is unlikely
to be resolved with more iterations, but you can try!

usemissing requests that the estimation incorporate information from
variables in the scale with missing values if the missingness can be assumed to
be Missing at Random or Missing Completely at Random; i.e., the reason that the
data are missing is not related to the scale score (see Schafer and Graham,
2002).

reverse specifies variables to be treated as reverse coded (i.e., their
values are predicted to be negatively correlated with the majority of the other
items in the scale). By default, the program will use the absolute value of the
loadings of any variables that appear to be reverse coded (i.e., those with
negative factor loadings) to estimate the scale reliability. As such, this
option should rarely be necessary. In rare cases, noreverse could be used
to force the program not to use the absolute value. However, this option is only
provided for advanced users who have a specific reason to desire the possibility
of negative factor loadings.

Examples

Basic example to calculate reliability

webuse bg2

omegacoef bg2cost1-bg2cost6

Variables with values that are missing at random

webuse cfa_missing

Without using the variables with missingness: omegacoef test1-test4

Using all information: omegacoef test1-test4, usem

Stored results

omegacoef saves the following in r():

Scalars:

r(omega) the estimated reliability coefficient

r(k) the number of items in the scale used to estimate reliability

References

Hayes, A. F., & Coutts, J. J. (2020). Use omega rather than Cronbach’s
alpha for estimating reliability. But….
Communication Methods and Measures, 14(1), 1–24.
https://doi.org/10.1080/19312458.2020.1718629

McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence
Erlbaum Associates.

McNeish, D. (2018). Thanks coefficient alpha, we’ll take it from here.
Psychological Methods, 23(3), 412–433.
https://doi.org/10.1037/met0000144

Raykov, T. (1997). Scale reliability, Cronbach’s coefficient alpha, and
violations of essential tau-equivalence with fixed congeneric components.
Multivariate Behavioral Research, 32(4), 329–353.
https://doi.org/10.1207/s15327906mbr3204_2

Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the
state of the art. Psychological Methods, 7(2), 147–177.
https://doi.org/10.1037//1082-989X.7.2.147

Author

Brian Shaw, Indiana University, USA

bpshaw@indiana.edu