reliability

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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 v9.omega$omega.lim [1] 0.858888

My questions regarding this example:

How does the interpretation between omega.tot and omega_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

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