Is my confirmatory factor analysis reliable if the variance-covariance matrix isn't positive definite?

CFA
1

I’m doing a confirmatory factor analysis on a Big Five personality dataset. I want to check if common method variance affects the correlations between the Big Five traits. Here’s my model:

bigFive_model <- '
  Extraversion =~ E1 + E2 + E3 + E4 + E5 + E6 + E7 + E8
  Agreeableness =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8
  Neuroticism =~ N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8
  Openness =~ O1 + O2 + O3 + O4 + O5 + O6 + O7 + O8
  Conscientiousness =~ C1 + C2 + C3 + C4 + C5 + C6 + C7 + C8
  CMV =~ E1 + E2 + E3 + E4 + E5 + E6 + E7 + E8 + A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8 + O1 + O2 + O3 + O4 + O5 + O6 + O7 + O8 + C1 + C2 + C3 + C4 + C5 + C6 + C7 + C8
'

bigFive_cfa <- cfa(bigFive_model, data = survey_data, estimator = 'MLR')

I got a warning that the variance-covariance matrix isn’t positive definite. But the summary shows good fit stats. There are some negative loadings on the CMV factor, and Extraversion has a negative correlation with CMV. Can I still use these results? Is my model wrong?

2

hey jack, that’s a tricky situation. non-positive definite matrix is def a red flag. maybe try simplifying ur model first? drop the CMV factor and see if that helps. could be too much overlap with the big five traits. fit stats can be misleading sometimes. might wanna chat with a stats pro if ur stuck. good luck mate!

3

Your CFA situation is quite complex, and the non-positive definite matrix is a red flag. While good fit stats are encouraging, they don’t necessarily validate a problematic model. The negative loadings on the CMV factor and its negative correlation with Extraversion are concerning.

These issues could stem from model misspecification or multicollinearity among your variables. The CMV factor, in particular, might be causing problems by overlapping too much with the Big Five traits.

I’d suggest a few steps:

  1. Check for multicollinearity in your data.
  2. Try a simpler model without the CMV factor first.
  3. If needed, use exploratory factor analysis to understand the underlying structure.
  4. Consider using alternative estimators or Bayesian methods.

Remember, a theoretically sound model is crucial. Don’t rely solely on fit statistics, especially with matrix issues. It might be worth consulting with a statistical expert for this complex analysis.

4

Hey Jack, that’s a pretty interesting study you’ve got going on there! :brain:

I’m no stats expert, but I’m super curious about your project. Have you considered that maybe the CMV factor is causing some trouble because it’s kinda doubling up on all the other traits? Like, it’s using all the same items as the Big Five, right?

What if you tried something different? Maybe you could use a separate set of items just for the CMV factor? Or even use a different method altogether to check for common method variance?

I’m really interested in personality stuff. How did you choose the Big Five model for your study? And what made you want to look into common method variance specifically?

Keep us posted on how it goes! It’d be awesome to hear what you end up figuring out. Good luck with your research!