<p>Part of the problem is that there are two different omega coefficients.  Omega_h and Omega_t.  I just checked semTools and they seem to report omega_t (which they label as omega).  </p>

<p>psych reports both.  With the example data set from semTools, the answers are similar, but not identical.  I suspect the difference is the psych version allows cross loadings and the sem version does not.</p>

<blockquote>
  <p><code>reliability(fit)
            visual   textual     speed     total
  alpha  0.6261171 0.8827069 0.6884550 0.7604886
  omega  0.6253180 0.8851754 0.6877600 0.8453351
  omega2 0.6253180 0.8851754 0.6877600 0.8453351
  omega3 0.6120052 0.8850608 0.6858417 0.8596204
  avevar 0.3705589 0.7210163 0.4244883 0.5145874</code></p>
</blockquote>

<p>summary(omega(HolzingerSwineford1939[7:15],covar=TRUE))</p>

<p><code>Omega 
Alpha:                 0.76 
G.6:                   0.81 
Omega Hierarchical:    0.44 
Omega H asymptotic:    0.52 
Omega Total            0.85</code></p>

<p>...
<code>Total, General and Subset omega for each subset
                                                 g  F1*  F2*  F3*
Omega total for total scores and subscales    0.85 0.89 0.65 0.71
Omega general for total scores and subscales  0.44 0.27 0.24 0.17
Omega group for total scores and subscales    0.35 0.62 0.40 0.54</code></p>

<p>For a discussion of various estimates of reliability see the article on PsyArXiv preprints:  reliability from Alpha to Omega    <a href="https://psyarxiv.com/2y3w9/" rel="nofollow noreferrer">preprint of reliability article available from psyArXiv</a></p>
Calculating McDonalds Omega with ::psych oder ::semtools
<p>Additionally to reporting Cronbachs Alpha, I would like to report McDonals Omega for each scale of my survey. I know that there are two ways to get Omega in R - either with the psych command omega()  which is for exploratory analysis or with reliability-command in semtools which is for confirmatory analysis. Because I have difficulties calculating the latter, I would like to know whether the results of both omegas are identical in terms of value?</p>

<p>Thanks in advance! </p>

<p>Carolin</p>