How to do a factor analysis with just one component?

Question

I have done a questionnaire with six questions to measure engagement. This is the only component I measure. To make sure they measure just one component, I tried to run a Factor analysis with Direct Oblimin. However, when I run the test it will not show a pattern matrix. (Is this because I have only one component? If yes, is this reliable enough to continue with a reliability analysis?). When I add a random variable it shows the pattern matrix with two components.

When I skip the Factor analysis and just start with a Reliability analysis: I increase my Cronbach's Alfa by deleting two items. My Cronbach's Alfa is .79 which should be fine for this experiment.

Answer 1

1. Are you doing a PCA or an EFA? You say that you do a factor analysis and use a direct oblimin rotation, but you also note that you are extracting components. PCA and EFA rely on different theoretical assumptions, and one should not use an oblique rotation for a PCA, as it goes against the fundamental point of the PCA—to maximize interindividual differences.

2. What software/packages are you using? What output you get is somewhat determined by what the programmers thought necessary given one factor extracted.

3. What are the eigenvalues? What does the scree plot look like? If it is extracting one factor, and there is an obvious elbow at the second eigenvalue, then extracting one factor seems reasonable for these six questions.

Answer 2

I can't really say without looking at your loadings or the corresponding eigenvalue of your single factor. If I had to guess, though, your issue might be that your items are not that related. Just running a single factor should give you no trouble.

Again, take this with a grain of salt since its a little tough to evaluate a factor analysis without the corresponding loadings.