Raykov's scale reliability estimate
Message/Author
 Tammy Kochel posted on Thursday, January 29, 2009 - 9:24 am
In MPlus version 5.2, is there a simple way to compute Raykov's CFA-based estimate of scale reliability? I am running a CFA within a SEM with categorical observed variables using WLSMV. Also, one of my factors is a second-order factor. If this cannot easily be done, is there an alternative statistic that you recommend for estimating the reliability of the scales?
 Linda K. Muthen posted on Thursday, January 29, 2009 - 3:35 pm
I am not familiar with this scale reliability. It is not automatically available in Mplus.
 Boliang Guo posted on Friday, January 30, 2009 - 2:23 am
I would suggest you useing 'Model constraint' command to calculate the reliability following Raykov's formula.Mplus' 'model constraint' command is a very useful tool!!
 Tammy Kochel posted on Friday, January 30, 2009 - 6:18 am
Dr. Raykov asked that I post this response:

“If I may come in, for continuous or approximately so items, pls. see my paper in the "British Journal of Mathematical and Statistical Psychology", 2008 (November issue, I think), where you may wish to use MLR as a method of estimation.

For categorical items, I don't have a solution that's nearly as simple. We are currently working on an extension to the case of binary items.

More generally speaking, if your items are loading nearly uniformly on a single factor, and there are no error covariances, alpha will be close to total scale score reliability (e.g., my 1997 paper in "Multivariate Behavioral Research"), so you can use alpha.

If you have a 2nd-order factor model, it may be reasonable to consider the sum or weighted scores for the items loading on each of the 1st-order factors, as 'scale components' themselves, which may be approximately continuous, thus reducing the case to that in the 1st para of this message. (If you decided to use weightes sum, the weights would come from using the concept of 'maximal reliability'--they are lambda/error variance, for each continuous item, or lambda for each item, form the logistic model fitted for binary items; e.g., Bartholomew & Knott, 1999, "Factor analysis and latent variable models", London: Arnold.)

Hope this helps.

Tenko Raykov, Michigan State”
 Paola Pascual-Ferra posted on Friday, March 15, 2013 - 6:40 pm
Hello. I am trying to estimate reliability of a scale using Raykov's formula. The variables are all continuous variables. I am taking each component in the formula

[(sum of unstandardized factor loadings)squared + sum of measurement error variances + (sum of nonzero error covariances)*2]

from the following tables in the output:

unstandardized measurement error variances (from the unstandardized Residual variances table)

nonzero error covariances from the model results after allowing the error terms to freely covary

However, I am not getting the results expected for the noncongeneric measure. I just wanted to verify with anyone in this forum who might be able to help me if I am getting the numbers from the appropriate tables.
 Bengt O. Muthen posted on Saturday, March 16, 2013 - 12:16 pm
You should square each loading before summing them, not squaring the sum.
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