I have a model which consists of 19 questions, which are divided in three factors (factor 1 – nine questions, factor 2 – six questions, factor 3 – four questions). For this I did a factor analysis and saved factor scores (computed by regression method) as variables.
But these three factors measure one big construct, to me. Now I was wondering if I can put the three created scores variables in a factor analysis again and extract one factor this time and save its factor scores as a variable, – to measure the overall construct.
Is this correct/possible to do?
** additional information **
To give some aditional information: I extracted the factors based on 'maximum likelihood', with a promax rotation. Saved these scores as regression variables, put those three variables in the factor analysis (SPSS). With the same method and was wondering if that would be a good construct.
In this case I factored, innovativeness (9 items), pro-activeness (6 items) and risk taking behavior (4 items). And I wanted to measure the overall construct, Intrapreneurial Behavior (IB) in this way. What do you suggest, how to deal with this issue to create a construct for IB?
Best Answer
Of course, it's "possible" to do what you're asking. The question is whether or not this is the best way to deal with the issue. You have left out mention of a number of important considerations: first, did you rotate a PCA to create a CFA with 3 factors? That you've noted "cfa" as a keyword, suggests rotation. To me, this means "common factor analysis." Is that correct?
One thing that often gets ignored about unrotated PCA is that it results in a mathematically unique solution where the first factor has been called a "junk" factor by some academics insofar as everything loads on it. Rotation cancels uniqueness by adjusting the loadings across the retained factors to something called "simple structure." The goal of simple structure is that each variable load on a single factor only and be zero (or close to it) for the other factors. Given that, have you examined the first, unrotated PCA component for its value wrt your objective?
Next, factor analysis results in a set of linear combinations that recover a reduced percentage of the total variance. A second, higher-order factor analysis would reduce the recovered variance even more.
Finally, if you want to get really geeky, check out the literature on additive and ultrametric trees for a good discussion of second-order factor analysis. This is not an area that's seen much recent research that I'm aware of but there's a Sage book with this title by James Corter that dates back 25 years or so.
In my opinion, leveraging the first PC would be a safe, easy solution.