Solved – CFA: negative factor loadings

Question

I found that after running a CFA, positive factor loadings and negative factor loadings occurred as appropriate. (An item representing a high score and an item representing a low score on the same construct loading in opposite directions.)

• Is it okay to leave these loadings as negative when other loadings on the same factor are positive?

• Or do these negative loadings mean that the an item is loading on the correct factor but will need to be reverse coded?

• If so, how does one reverse code a continuous variable in R, when it is taken to 2 decimal places? (e.g. can't just say 1 = 6, …., 6 = 1 with values like 2.43)

Answer 1

You are correct: the negative loading suggests a negative linear association between the latent variable and the observed variable, and if you were to compute an observed score to approximate the latent variable (e.g., by summing or averaging items), it would be appropriate to reverse-score the negative loading variables. As for how you could take this negative loading into account when creating a score for your variable, I see you as having three options:

1. Keep the model in latent space: whatever analysis you are attempting to do, if you can, you should try to do it using some form of latent modelling. That way, you have no need of having to reverse score anything to create an observed score of your factors, and you also get the associated perks of latent models (see here for a discussion of some of them).
2. Use factor analysis methods to estimate factor scores: This can be done either using EFA or CFA approaches. Granted, there will be legitimate concerns about the determinacy of your estimated scores, but at the very least, the scoring algorithms will take into account the negative loadings for you, so you don't need to worry about how to handle them yourself.
3. And finally, Standardize your variables, then reverse score: if you can standardize your variables, before trying to create a sum/average score, then reverse-scoring is easy; just flip the sign. But then by doing so and using sum/average scores, you'll lose all the benefits of latent variables or estimated factor scores.