How to Calculate Composite Reliability for SEM Model

I have discussed earlier that reliability of indicators can be explored by calculating Cronbach’s alpha, but this test has had its detractors. Yang and Green (2011) has noted that Cronbach’s alpha is known to overestimate and underestimate values and is “not to be construed as a coef- ficient of internal consistency but rather an estimate of reliability based on the internal con- sistency of items” (p. 389). In the face of this criticism, a test called “composite reliability” has been offered as a better alternative to Cronbach’s alpha, especially when using SEM (Hair et al.2009). This reliability test is calculated based on the factor loadings of indicators obtained from a confirmatory factor analysis. The only downside to this test is that AMOS does not calculate composite reliability and so you have to calculate it by hand (or, if you are savvy enough, design a script to calculate it). To calculate composite reliability, you need the standardized factor loadings of each construct. Here is how to calculate a composite reli- ability for each construct:

For example, let’s take the construct of Adaptive Behavior. Standardized Factor loadings from the CFA

Adapt1 = .896

Adapt2 = .920

Adapt3 = .872

Adapt4 = .875

Adapt5 = .869

An indicator’s measurement error is calculated by taking 1 minus the R2 value for an indicator of a construct (this is the variance you are not explaining).

The composite reliability for the Adaptive Behavior construct is .94.You may notice that the composite reliability technique and Cronbach’s alpha will produce slightly different values. Though Cronbach’s alpha may the easiest and most widely used analysis for reliability, I find composite reliability to be a better representation of the reliability of indicators when the measurement model is included as well.

Source: Thakkar, J.J. (2020). “Procedural Steps in Structural Equation Modelling”. In: Structural Equation Modelling. Studies in Systems, Decision and Control, vol 285. Springer, Singapore.