Hello Guys,
I'm performing factor analysis in SPSS with 168 observations of likert-scale variables, EFA generates two factors, thus Factor 1 includes 3 variables and loading scores are high (0.777, 0.785, 0.421) and so the composite realibility and extracted variance, around 0.8. However, cronbach Alpha for internal consistency showed value of only 0.52.
The Factor 2 showed good values for all three measures, so the only problem is internal consistency of the Factor 1. The discriminant validity between two factor is also good. KMO of whole construct is around 0.75.
In this case, can I consider this "problematic" factor as "valid"? Otherwise, what can I do to solve this issue?
The idea is to use them within Structural Equation Modelling later. Thank to all of you in advance!
Hello Andrei
In my understanding, the construct validity is achieved however the reliability remains a concern. One way to handle this could be to observe what happens when you remove a particular item and see the change in the value of alpha. If there is an increase in the alpha value and the other parameters of EFA are also at acceptable levels, then alpha of nearly 0.6 would serve the purpose.
Andrei Mikhailov Cronbach's alpha is a meaningful measure of composite reliability (reliability of the sum or average of measures) only under the assumption of (at least) essential tau equivalence as defined in classical test theory (CTT). Essential tau-equivalence means your items are (1) unidimensional (i.e., they measure only one factor with uncorrelated error variables) and (2) have equal weights on that single factor (equal unstandardized factor loadings, no cross-loadings onto other factors). These assumptions cannot be tested with EFA, but they can be tested with confirmatory factor analysis (CFA). When the measures do not satisfy these criteria, Cronbach's alpha may be underestimating their composite reliability and/or may be completely misleading as a measure of composite reliability. Alpha also implies that your measures are continuous (measured on an interval scale).
Alpha itself is not a measure of unidimensionality or homogeneity. It can be high or low for item sets that are uni- or multidimensional. I personally therefore find the term "internal consistency" to be problematic because it suggests that alpha can tell you how homogeneous your items are (which is not the case). Alpha really is a measure of composite reliability under the assumptions given above--not more and not less.
In addition, I would be skeptical about the item with the rather low (standardized?) loading (.421). Often, such a low loading suggests that this item measures something different from the others, at least in part. What do the cross-loadings of the items look like in the EFA solution? And did you use EFA or PCA?
Dear Andrei Mikhailov
I largely agree with Christian Geiser comments. However, I would like to point out that cronbach's alpha can also be calculated when the measures are ordinal and not continuous. It is important to verify the (at least) essential tau equivalence hypothesis, as this may affect the value of the calculated coefficient. If you work with R, I recommend using the coefficientalpha package (https://cran.r-project.org/web/packages/coefficientalpha/index.html) which allows you to test the above hypothesis. For more information see Article Robust Coefficients Alpha and Omega and Confidence Intervals...
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