I am examining results from an exploratory factor analysis (using Mplus) and it seems like the two-factor solution fits the data better than the one factor solution (per the RMSEA, chi-square LRT, CFI, TLI, and WRMR). Model fit for the one factor model was, in fact, poor (e.g., RMSEA = .10, CFI = .90). In the two factor model, the two latent factors were strongly correlated (.75) and model fit was satisfactory (e.g., RMSEA = .07, CFI = .94). The scree plot, a parallel analysis, and eigenvalue > 1, however, all seem to point to the one-factor model.
I am not sure whether I should retain the one or two factor model. I'm also not sure whether I should look at other parameters/model estimates to make determine how many factors I retain. Theoretically, both models make sense. I intend to use these models to conduct an IRT (uni- or multidimensional graded response model - depending on the # of factors I retain).
Thank you in advance!
If I remember correctly, Mplus gives you Chi-square-difference tests between models when running EFA. Those are very informative for choosing the best model.
If you are concerned about there being common variance in addition to specific variances, I would recommend looking into bifactor models (of which second-order models are a restrictive special case).
To Philipp K. Masur , Gregory Camilli , & Heiko Breitsohl these are all incredibly thoughtful and helpful responses to my question. The poor model fit of the 1-factor model seems to suggest other sources of common variance exist. I shall proceed with bi-factor EFA and then use mulidimensional IRT modeling (bi-factor IRT).
You might want to try confirmatory factor analysis with a single latent variable but with correlated measurement errors, and compare that to a 2-factor model (with or without correlated errors, while estimating the correlation between the two latent factors). See Bollen and Grandjean, American Sociological Review 1981, for an example of this approach.
As far as I know, IRT usually employs pretty strong assumptions. I tend to use CFA instead, so I can pick and choose which assumptions to employ as constraints, and which to relax and estimate. So I'm inclined to think CFA with correlated measurement errors is an alternative to an IRT approach, but maybe there's a way to combine the two. Wish I could be more help on that question.
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