I performed an exploratory factor analysis on a set of items. Most of these items loaded onto one of five factors, but a few of them did not load onto any factor.
The first time I did this, I chose the 'Save as variables' option, using the Anderson-Rubin method, and performed subsequent analyses on the newly-created variables.
Out of curiosity, I repeated the process, but instead of saving the factors as variables, I simply noted which items loaded onto which factors, and then created new variables to represent the average score for the items in each factor (all items had a common response format). I then re-performed the analyses using these variables.
I noticed that the results of my subsequent analyses were mostly the same, but not entirely. So which is the most valid way of representing the factor for further analysis, following the factor analysis? Why do the two methods lead to slightly different results?
You can go either way. If the factor loadings on each factor are not too dissimilar, an easy option is to create a simple summative score.
Either save factorscores or proof a sumscore is sufficient with the items you want to sum. In Rasch or Mokken the sumscore is supposed to be a sufficient and necessary statistic. One can test if a set of items can be summated in SPSS reliability by asking for the additivity test, but usually it will fail. If you perform a factoranalysis, one would need to get the factorscores. Even small difference may lead to big problems. If a rocket would be launched and it would miss its destination by 1% it could end up getting blurred pictures. It is the reason I prefer Rasch and Mokken above doing a factoranalysis.
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