Role of Cronbach's alpha in scale dev... PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Kurt posted on Wednesday, November 04, 2009 - 8:50 am
I'm using CFA to confirm the dimensionality of a construct and develop subscales to measure each dimension (i.e., factor).

I plan on reporting subscale scores.

What role should Cronbach's alpha play, if any, in scale development? Or should it's use be restricted to simply reporting reliabilities of subscales, *after* they have been developed based on factor loadings, etc.

I'm aware that Cronbach's alpha assumes:

- no residual correlations
- that items have identical loadings
- unidimensionality

I've confirmed unidimensionality (for each subscale), and will probably rule out correlated errors, so is it appropriate to report Cronbach's alpha for each subscale? How "identical" do the loadings need to be for Cronbach's to be accurate?

Thanks for your insights.
 Linda K. Muthen posted on Wednesday, November 04, 2009 - 5:47 pm
I believe there has been a recent debate about Cronbach's alpha versus some more modern measures. You might want to check the SEMNET archives or ask about it on SEMNET.
 Sean Mullen posted on Friday, November 06, 2009 - 2:41 pm
Hi Kurt,
See Psychometrika's March issue (2009) where Sijtsma and others have discussed alternatives (i.e., "glb") to Cronbach's alpha; see also Raykov (in BJMSP, 2007 & 2008).
 Linda K. Muthen posted on Saturday, November 07, 2009 - 11:54 am
Following is a post on this topic from Tenko Raykov:

"Someone asked recently what role coefficient alpha should/could play in scale development. In general, it can mislead seriously. See Raykov, Br. J. Math & Statist. Psychol., 2007, 2008, where also a generally applicable latent variable modeling method is outlined for estimating scale reliability and criterion validity, in particular using Mplus. (The approach has certain assumptions that need to be fulfilled in order to be applied.)

The exception to the above statement of alpha possibly being misleading in scale development, is the case of uniformly high factor loadings, no error covariances, and unidimensional instrument. Then alpha is essentially the same as reliability (in the population; see e.g., Raykov, Multivar. Beh, Res., 1997, for details)."
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