After browsing cross validated and several other sources on the web, I still cannot get a grip on McDonald's Omega as a measure of internal consistency. I have a hunch that many fellow social scientists feel similarly insecure about the measure, so I hope to get some clarification on several aspects on this measure:
Assumptions / Prerequisites
While the assumptions for Cronbach's Alpha are commonly discussed (e.g. Cronbach Alpha Assumptions), I haven't managed to get a full picture of the prerequisites for McDonald's Omega. My questions being:
- What are the general assumptions underlying Omega?
- Is there a rule of thumb regarding sample size, or a ratio between variables and observations that should be considered?
- Is Cronbach's Alpha superior to Omega under any circumstances at all?
Coefficients and Interpretation
Secondly, it appears that there still is a great deal of confusion around the different Omega coefficients, perhaps most notably returned by the psych
-package in R. For clarification, maybe someone could offer a full interpretation of coefficients in the following example, in ?psych::omega
,
library(psych)
#create 9 variables with a hierarchical structure
v9 <- sim.hierarchical()
#find omega
v9.omega <- omega(v9,digits=2)
> v9.omega$omega.group
total general group
g 0.7984002 0.6857363 0.1126608
F1* 0.7449332 0.6034008 0.1415325
F2* 0.6303512 0.4034189 0.2269323
F3* 0.5022309 0.2460886 0.2561423
> v9.omega$omega.lim
[1] 0.858888
My questions regarding this example:
- How does the interpretation between
omega.tot
andomega_h
(general) differ in this example? Or: What would the correct global measure of internal consistency for the entire measure/questionnaire be? - What is
group
telling us? - When is
omega.lim
relevant?
In addition: It appears that omega_h
(general) is getting the most attention in posts/reports, but these values always strike be as surprisingly low in almost every example I have seen. How come?
Thanks
Best Answer
The topic is old, but the questions interesting, so I would like to include some of available information regarding some questions.
Statistical requirements/assumptions underlying Omega:
Rule of thumb regarding sample size, or a ratio between variables and observations that should be considered?
Similarly, the sample size should follow the CFA sample size definition, using preferably simulation methods, as those enabled by
R simsem package
.An interesting reference for this discussion is available on: Brunner M, Nagy G, Wilhelm O. A tutorial on hierarchically structured constructs. J Pers. 2012;80(4):796-846. doi:10.1111/j.1467-6494.2011.00749.x