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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? Thank your for your help!

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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. – StasK Sep 26 '12 at 14:16

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