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Can one do a confirmatory factor analysis with items on different response scales. let's say 50 items have a likert response scale from 1 to 4, and the second group of items have a likert response scale from 1 to 5.

From my understanding, for exploratory factor analysis, this is not a problem, especially if I estimate the EFA on a correlation matrix. Am I right to assume this?

I am not quite sure about the CFA, whether this is okay. Any pitfalls, considerations, most responses I find online just beat around the bushes and I can't make my mind up based on them.

Thanks

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CFA is fine with items using different scales. Factor analysis in your case isn't even an analysis of variables, but is an eigendecomposition of the correlation matrix of the variables with the diagonal identity vector replaces with communality (shared variance) estimates, so the distribution of individual variables is largely irrelevant.

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