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I have a doubt regarding confirmatory factor analysis (CFA). I have three different constructs, each one with its corresponding scale:

  1. resilience (3 dimensions, 4 items each)
  2. humour (3 dimensions, 4-5 items each)
  3. coping (2 dimensions, 8 items each)

My question is: do I have to perform a different CFA for each construct (one for resilience, one for humour and another one for coping, separately)? Or do I need to perfom a single CFA testing for the three constructs simultaneously, establishing correlations (double-headed arrows) between the different dimensiones of resilience, humour and coping?

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    $\begingroup$ Doesn't matter; the larger model will likely have a worse fit, as you may be discovering unpleasant cross-loadings. The inferential framework of chi-squares and p-values assumes you've only fitted one model once. Any sidesteps, formally speaking, would obligate you to perform correction for multiple testing. People in SEM don't bother, and that's one of many reasons this field is so plagued with ad-hoc approaches inconsistent with one another, inconsistent internally, and lead to irreproducible results. $\endgroup$
    – StasK
    Sep 26, 2012 at 14:16
  • $\begingroup$ What about when testing for discriminant validity by comparing Chi-square? Would you constrain only the pair of constructs of interest and leave the others unconstrained? Or would you only include the pair of constructs of interest in the analysis? $\endgroup$
    – user59205
    Oct 25, 2014 at 19:51

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You can do a confirmatory factor analysis of the whole thing. This is preferable, although as @StasK notes, most likely your model will be rejected because of things like items not perfectly loading onto only one factor. This is very common, and it shouldn't necessarily bother you too much. You can look at the root mean squared error of the approximation (RMSEA) to see how well your model approximates the data, despite the fact that your model won't be exactly correct.

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