I am trying to evaluate my measurement model in a SEM with all binary indicators with a confirmatory factor analysis.
How do I compute the variance explained , Cronbach's alpha, KMO and the Bartlett test of sphericity for each latent construct in MPlus?
bmuthen posted on Thursday, October 03, 2002 - 9:23 am
One approach is to apply the same techniques used for continuous indicators (I will not attempt to state these here, but see the literature). That is, treat the y* variables as observed variables. One can, however, argue that this y* approach does not capture the relationships for the observed y variables. I don't know if anyone has done work on this for binary y's without relying on y*'s. Perhaps other Mplus Discussion readers would know.
Saul Cohn posted on Saturday, February 25, 2006 - 12:28 pm
After you have your latent construct what do you do next in research project. Do I need to use Cronbachs alpha to see how reliable they are?
bmuthen posted on Sunday, February 26, 2006 - 5:54 am
I don't see Cronbach's alpha as an important statistic to consider in factor analysis contexts. If you want to know how well your factor is measured you want to look at factor determinacy. For definitions and further insights, see the latent variable literature, e.g. Bollen's book.
I would like to learn more about why you do not think Cronbach's alpha is an important statistic in factor analysis. Do you have any references you could provide me or would you mind briefly summarizing your argument?
The Cronbach alpha reliability has to do with the correlation between the sum of items and a factor, where it is assumed that there is only 1 factor behind the items and the items have the same loadings and there are no residual correlations. See Bollen's book, p. 217. With different loadings there are different alternatives - see Bollen and more recently Tenko Raykov's work.
My feeling is that you instead want to use factor analysis and ask how well the factor is measured, e.g. by factor determinacy. Using SEM, the real question is how small the SEs for structural coefficients can be as a function of good indicators (high determinacy) for the factor. If you insist on using a sum, it is of course useful to know its reliability, but then why not derive it from the factor model used to establish unidimensionality.
Iryna posted on Wednesday, September 01, 2010 - 9:26 am
Hello, How can I compute Cronbach Alpha in Mplus? (the input data is a table of corelations between items) Thank you.
Here are my critical comments on the use of Cronbach's alpha:
Cronbach's alpha can be mentioned for historical reasons as yet another reliability index, although a flawed one. The index is not derived from parameters of a factor model but uses the variances and covariances among the items (see, e.g., Raykov, 2012). When the items are unidimensional and at least tau-equivalent, and with uncorrelated residuals, this index is valid, but is otherwise problematic. The use of the Cronbach alpha index as either a reliability or internal consistency index has been strongly criticized in the psychometric literature; see, e.g. Sijtsma (2009) and Raykov (2012).