[Stata] Calculating McDonald’s Omega

How it is different from Cronbach’s alpha?

📒 Dunn, T. J., Baguley, T., & Brunsden, V. (2014). From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation. British journal of psychology, 105(3), 399-412.

McDonald’s omega and Cronbach’s alpha are both measures of internal consistency reliability, which is the extent to which items in a scale are interrelated and measure the same construct. However, there are several differences between the two coefficients.

1. McDonald’s omega is based on a factor analytic approach, whereas Cronbach’s alpha is primarily based on the correlation between the questions. This means that omega is less sensitive to the number of items in a scale and the distribution of item scores. Omega also provides separate estimates of the reliability of the general factor and the group factors.
2. McDonald’s omega is more robust than Cronbach’s alpha against deviations from the assumptions of tau-equivalence and uncorrelated error variances. This makes omega a more suitable measure of internal consistency in many situations.
3. McDonald’s omega is less biased than Cronbach’s alpha when the number of items in a scale is small or when the items are not tau-equivalent. This means that omega is a more accurate estimate of internal consistency in these situations.

To calculate McDonald’s omega in Stata, you can use the omegacoef command created by Dr. Brian Shaw. This command estimates the scale reliability of a test using McDonald’s omega coefficient, which has many desirable statistical properties that make it preferable to the widely used Cronbach’s alpha.

Calculating McDonald’s Omega in Stata: omegacoef

Here are the steps to calculate McDonald’s omega using omegacoef command:

Step 1. Install the omegacoef command

ssc install omegacoef

Step 2. Estimate the factor analysis model with sem command

The important step for omegacoef command is to run sem command before running it. Let’s say that your summary variable (scale) name is depression and the list of items are phq1–phq9. You can run confirmatory factor analysis using sem command as follows.

sem (depression -> phq1 phq2 phq3 phq4 phq5 phq6 phq7 phq8 phq9)

One thing to note is that you need to use the lower case variable names for the list of variables after (->). Here, the list of items refer to phq1-phq9. The general command could be as follows, but you should adapt it for your dataset.

sem (scale -> var1 var2 var3) 

If you skip this step 2, the omegacoef command will return the error message like “model is not specified.”

Step 3. Run the omegacoef command 

omegacoef var1 var2 var3 

The output of the omegacoef command will include the estimated McDonald’s omega coefficient.