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In the omega function in the psych package for R, we have several outputs including Hierarchical omega, Asymptotic omega and Total omega.

I was reading about the outputs, but I find nothing about what the asymptotic omega means. For an analysis, a friend of mine calculated an omega H = 0.70 and an asymptotic omega of 0.98. I'd rather not ignore this big asymptotic omega.

Can somebody explain what the asymptotic omega is and how it is different than the hierarchical omega?

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    $\begingroup$ I don't see an R package called "omega". I did find a function, ?omega, in the psych package, & the Omega Project. Is 1 of those what you're referring to? Can you edit your Q w/ a link to the package &/or function that's confusing you? $\endgroup$ Dec 29, 2012 at 18:39
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    $\begingroup$ Just added the comment. Thx! $\endgroup$ Dec 30, 2012 at 2:21
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    $\begingroup$ the function omega has two references associated with it, unfortunately neither appear to have a freely available copy so I can't see if they answer your question. I do recommend checking these out in the first instance as typically the references for a function will have descriptions of what it is and why one should use it $\endgroup$ Dec 30, 2012 at 11:31

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From the documentation:

Another estimate reported is the omega for an infinite length test with a structure similar to the observed test. This is found by $$ ω_{\rm limit} = \frac{ \vec{1}\vec{cc'}\vec{1}}{\vec{1}\vec{cc'}\vec{1} + \vec{1}\vec{AA'}\vec{1}'} $$

Following suggestions by Steve Reise, the Explained Common Variance (ECV) is also reported. This is the ratio of the general factor eigen value to the sum of all of the eigen values. As such, it is a better indicator of unidimensionality than of the amount of test variance accounted for by a general factor.

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    $\begingroup$ Welcome to the site, @Jon. This does answer the question of what asymptotic omega is, but I think the OP might like to know a bit more. Eg, which omega should the OP use? Would you care to elaborate on this a little bit? $\endgroup$ Jan 10, 2014 at 22:05
  • $\begingroup$ So... as for the added response... does that mean asymptotic omega can't be used for reliability? $\endgroup$ Jan 25, 2017 at 10:48

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