PCA Rotation confusion

[Philippe Caeyers]

Hello,

I'm rather new to PCA, and I'm struggling to interpret and move forward with my output. The goal is to create a single proxy of bank risk using many bank-level variables (create a total score using the component factor scores). My struggle is with the the output after rotation (varimax).

The benefit of rotation is that it become more easily to categorize and 'label' component. However, it does not seem straightforward here as the factor loadings are rather 'dispersed' and 'overlap' across traditional risk categories. Should I refrain from trying to categorize, take the output as it is and create my total risk scores? Or does this dispersion undermine the validity?

[Phil Bromiley]

There is a massive literature on principal components and another massive literature on factor analysis.

The normal interpretation of this kind of result would be that you have six different components, rather than the one you are trying to make one. You do have some variables that don't load in the obvious way, but this is pretty normal. At least you don't appear to have any big loadings where the same variable loads on more than one component.

That the components don't completely align with variables is probably a good thing. There's not much point in doing a PCA simply to find that the capital variables associate with one another and the management variables associate with one another and that liquidity variables associate with one another. I did something similar in a paper with Kent Miller back in 1990.

Most traditional measurement assumes you have on unobserved construct that influences the observed variables. However, there is also a class of measures where the overall measure is a sum of the observed variables. For example, my wealth is a sum of the value of my house, the value of my bank account, etc. There is no reason that these components should be highly correlated but wealth is still a legitimate construct.

It sounds as if you are trying to use this second concept of a measure by seeing firm risk as the sum of different kinds of risk. That is certainly plausible, although it has been done a great many times in the past.

[Philippe Caeyers]

There is a massive literature on principal components and another massive literature on factor analysis.

The normal interpretation of this kind of result would be that you have six different components, rather than the one you are trying to make one. You do have some variables that don't load in the obvious way, but this is pretty normal. At least you don't appear to have any big loadings where the same variable loads on more than one component.

That the components don't completely align with variables is probably a good thing. There's not much point in doing a PCA simply to find that the capital variables associate with one another and the management variables associate with one another and that liquidity variables associate with one another. I did something similar in a paper with Kent Miller back in 1990.

Most traditional measurement assumes you have on unobserved construct that influences the observed variables. However, there is also a class of measures where the overall measure is a sum of the observed variables. For example, my wealth is a sum of the value of my house, the value of my bank account, etc. There is no reason that these components should be highly correlated but wealth is still a legitimate construct.

It sounds as if you are trying to use this second concept of a measure by seeing firm risk as the sum of different kinds of risk. That is certainly plausible, although it has been done a great many times in the past.

Thank you very much for your reply!