PCA and Cronbach's alpha

[Serena Menny]

Hello everyone,

I have 6 variables that I want to aggregate, so I conducted PCA to identify different dimensions before combining them into a single general variable. My question is: should I first calculate Cronbach's alpha or conduct PCA?

1. If I calculate Cronbach's alpha for the 6 variables together, I obtain a value of 0.7245, which is acceptable. Then, when I perform PCA, I find three dimensions. Should I also verify alpha for these three dimensions separately? One of them has an alpha value of 0.6799, which I assume is unacceptable.
2. Alternatively, if I conduct PCA first and identify these three dimensions, do I need to confirm their separate alphas? Additionally, when I aggregate them, should I calculate their combined alpha? Upon calculating the alpha for the three dimensions, I obtain a value of 0.4346

I'm feeling a bit lost, so I would greatly appreciate your assistance

Thank you,

[Maxence Morlet]

ssc install factortest

You may want to run the above command as well. Kronbach's alpha is informative, but not a make or break. There are other measures, and intuition is key as well.

[Nick Cox]

I am guessing that all these variables are potential predictors and that you also have an outcome or response variable. If that's not right, the following may need qualification.

I don't have a view on Cronbach (not Kronbach) before PCA or the other way round, but why does that matter? What does alpha tell you that the eigenvalues don't?

A PC is just a weighted linear combination of what is fed to it.

An alternative to all this is to feed all your variables directly into the regression. That is a way of getting ... a weighted linear combination of the predictors.

The pluses and minuses of different strategies include;

0. All these strategies are data-driven with each step depending on what comes out of the data.

1. Prior PCA of all predictors, or of groups of predictors, at best identifies how far the predictors agree with each other. That's nothing directly to do with how they relate to the outcome.

2. PCA doesn't guarantee clear and simple interpretation, but nothing does.

3. Throwing everything into the model may seem likely to be burn up degrees of freedom, and run the risk of over-fitting, but you can always simplify the model by throwing out predictors. What is your sample size?

In fields like yours (and mine, which is different) there is always a question of whether the theory is strong enough to allow it to dominate the data analysis (which is itself a loaded summary). Different researchers are typically highly negative about some other groups' approaches, and me too.