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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? Saul 

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. 


Hi, 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? Thank you! Alison 


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. 


I would Google Cronbach's Alpha and look for papers by Tenko Raykov. I think he has done this is Mplus. Look also at the literature that criticizes this measure. 

Joseph Dien posted on Thursday, March 07, 2013  2:34 pm



His 2010 book has full MPLUS code examples. 


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 tauequivalent, 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). 

Giulia Zardi posted on Wednesday, January 11, 2017  9:22 am



Dear All, I need to calculate KR(20) (since I'm working on dichotomous items) in MPlus. Is that feasible? If so, which is the code that I need to use? Thanks in advance! Giulia 


Please see the RaykovMarcoulides 2015 Ed & Psych Meas article. 


One of the answers above says: "My feeling is that you instead want to use factor analysis and ask how well the factor is measured, e.g. by factor determinacy." The factor determinacy does not seem to work with categorical variables in MPLUS. I wonder what the recommendation would be in this case, i.e. which measure(s) to use? 


A good way to see the quality of the factor score is to look at the plot of "information curves". This has to do with the precision (SE) of the factor score estimate (which unlike for continuous items varies across factor values). You can read about that in the Item Response Theory literature. 

John C posted on Wednesday, August 09, 2017  8:16 am



I would like to see if there is a way Mplus users are using to estimate an internal consistency coefficient in the case of ordered categorical indicators. For example, Bentler (2009) proposed such an approach based on the sum of the underlying normal variables. 


See our 3 Reliability FAQs on our website, especially Reliability  binary and ordinal items 

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