I am doing CFA in lavaan (3-factor model, all factors correlated). The fit of this model is quite bad and I wanted to improve it. I realized, that the full questionnaire contains four negatively-keyed items, and that they are all loaded under one factor (F3). So I wondered if the model fit might be bad because of the potential influence of this "method factor." I decided to allow residuals of these items to correlate with each other. The model fit improved immediately, but factor loadings of the items in F3 are really low now (0.2-0.5).

Could anyone tell, why this happened? Does it mean, that the respecified model is bad, or does it confirm the hypothesis, that there is some bias due to presence of negatively-keyed items?

Thank you!

Syntax Results Fit indices


1 Answer 1


Adding a residual correlation is equivalent to adding an additional factor.

If the loadings are reduce when you add this, it's because these items are in a separate factor. (Perhaps post your code and results? You say "I decided to allow residuals of these items to correlate with each other. " but I don't see how you can do that and keep the model identified.

Edit: If it's a method factor, a bifactor model might fit better.

  • $\begingroup$ OK, thank you. The negatively keyed-items are 4, 5, 10, 18, 19, four items are loaded on F3, one item loaded on F2. If I specify these correlated residuals, model converge normally and the fit indices are quite ok... Except of chi-square, yeah, but my sample size is big and data are skewed, so I expected that index to by significant. $\endgroup$
    – AnnaNams
    May 8, 2018 at 16:19
  • $\begingroup$ I believe it is not the case that adding a residual correlation is equivalent to adding another factor. It can be the same thing, but the residual correlation could be due to something like a testlet effect, e.g. you have higher residual correlations b/c of some very similar phrasing or because the questions were related to one particular reading comprehension passage. In that case, it need not be equivalent to adding another factor. $\endgroup$
    – Weiwen Ng
    May 8, 2018 at 16:37
  • 1
    $\begingroup$ Pasting code, not images, makes it much easier to do things like search and replace. $\endgroup$ May 8, 2018 at 17:45

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