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I was wondering why there are no standard errors and p-values reported for the factor loadings in the exploratory factor analysis, instead the magnitude of the factor loadings are used to judge the relative importance of the items. This is while both p-values and standard errors are reported in the outcome for the confirmatory actor analysis. This is regardless of the software use.

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    $\begingroup$ When there are more than 1 factor, different sets of loadings may be produced in EFA by different rotations of the factors. The solution (w.r.t. the loadings) is not unique. To make it unique, one has to fix some loadings, i.e. take them for granted. Then it is possible to estimate errors for the rest of the loadings. But which ones to fix - why to fix these and not those? And how many to fix - the necessary minimum or more? There is no sensible guideline for that. So software of EFA usually don't compute CI. With one-factor solution, some software does. $\endgroup$
    – ttnphns
    Sep 9, 2020 at 12:38

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In EFA, the model is not identified (underdetermined); there are multiple combinations of coefficients that produce an equally good fit. Therefore, it is not possible to estimate standard errors or $p$-values of individual coefficients. An analogy in regression would be perfect multicollinearity.

This is not the case in CFA; the model is identified and usually overidentified (overdetermined), and in the latter case it is possible to obtain standard errors and $p$-values of individual coefficients. An analogy in regression would be absence of perfect multicollinearity.

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