# Hierarchical Factor Analysis - Analyzing the factor structure of an identified factor

Problem Summary

After performing an exploratory factor analysis one of the resulting factors "contains" a lot of variables which make its interpretation very hard.

Since all the other factors have a very clear meaning (and consist only of a couple of variables) I wonder if there is a way to do another factor analysis just on the one identified big factor.

So my question is, what are valid approaches to do this sort of "hierarchical" or "multilevel" factor analysis?

Background

I am currently analyzing a brand study comparing the perception of several car manufacturers. In this study respondents rated car brands on >20 attributes on a scale of 1-7 e.g. Design, Competence in Electric Drives, etc.

The resulting data looks like this:

ID  Brand  Attribute_1  Attribute_2  Attribute_3  ...
p1  Ford   6            5            2
p1  GM     3            6            4
p2  Ford   2            2            2
p2  GM     4            2            6


Since >20 variables is a lot and many of them are correlated or represent very similiar concepts (e.g. Exclusive vs. Special) I explored the factor structure via factor analysis (via R).

The results are quite intuitive for most of the resulting factors. However the first factor contains most of the variables and can only be interpreted as "Generally good car brand".

This makes sense to me as the difference between the variables in this factor and the other factors identified is more significant (e.g. identified factors were very specific like "Digital Competence") and all the variables could be broadly described as "quality factors" of a car.

However I believe that even this overall "Quality Factor" contains a deeper level factor structure (e.g. Design vs. Performance). Therefore I would like to explore this factor structure as well but I do not know the best approach to this.

Approaches tried

So far the only way to tackle this problem I have come up with is to simply repeat a EFA on the variables loading high on the first factor. However this approach seems very "hacky" and I'd prefer to use an approach which acknowledges the identified factor structure of the first step and is more hierarchical in nature instead of just repeating the same analysis on a smaller data set.

I ran into a similar problem using PCA as the first identified component (explaining most of the variance) again only identifies variables that have the highest influence on overall "quality perception". Again the only way forward I know would be to redo PCA and leaving all the variables loading high on the other components out which again seems to be not ideal.