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I have a general question about factor loadings of items in Confirmatory and Exploratory Factor Analysis. Fitting a CFA model to a data set based on factor loadings (e. g. cfa() of the lavaan package) of an exploratory factor analysis will result in a CFA model. The output gives me estimates of factor loadings of all indicators, which are different for the same item, compared to the value they got for the same factor in EFA.

I would like to know, why is that the case? And which value should be considered for evaluating the "goodness of fit" of the item to the respective factor?

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  • $\begingroup$ Can you post code? $\endgroup$ – Jeremy Miles Mar 7 '17 at 20:47
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When you emulate an EFA in the CFA framework (E-CFA), you are creating a "hybrid" approach that is similar to maximum likelihood EFA but not identical. The loadings should be pretty close, though, so make sure you are doing all steps of the E-CFA correctly. Also make sure that you are comparing the results to maximum likelihood EFA and not some other version of factor extraction.

  1. Obtain a rotated maximum likelihood factor analysis solution
  2. Identify an "anchor item" for each factor (i.e., high loading and low cross-loadings)
  3. Constrain the cross-loadings to zero for each anchor item
  4. Set the factor variances to one
  5. Run the CFA model and examine the standardized results

E-CFA has some benefits over standard EFA in that it provides standard errors, statistical tests, and access to modification indices. You can also do multigroup comparisons and other SEM extensions.

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