I have performed a factor analysis of 14 binary items (Satisfactory vs Not Satisfactory) which yielded 2 factors with 7 items each. I am interested in creating simple factor scores by summing individual responses on the 7 items for each factors. Factor scores would then range from 0 to 7. I am then interested in correlating these scores with both a continuous and a binary variable.

My questions are about the appropriateness of this simple scoring methodology and how to treat these scores in subsequent correlational analyses (Pearson, Spearman, etc).

  • 2
    $\begingroup$ I think - You ought to have asked another question first, whether linear FA is appropriate for binary data at all. stats.stackexchange.com/a/19595/3277, stats.stackexchange.com/a/16335/3277 $\endgroup$
    – ttnphns
    Nov 22 '13 at 17:36
  • $\begingroup$ I should have noted that the FA was done in Mplus treating the data as binary $\endgroup$
    – user35179
    Nov 22 '13 at 18:43
  • $\begingroup$ Then please consult Mplus (a respectable package) documentation: how it did FA for your data, how it computes factore scores for such data. Then you are likely to be closer to answer your own question or to reshape it into more specific form. $\endgroup$
    – ttnphns
    Nov 22 '13 at 19:53

Don't call the unweighted item sums "factor scores". Even if the items were continuous and you were using a weighted sum, the scores would not be the same as, or even necessarily good estimates of, the theoretical factors in a factor analysis. Call them "scale scores" (or something similar). Such scales are the norm, rather than the exception, and treating them as equal-interval measures in further analyses is standard practice, even with as few as 7 items. The scales are far more than purely ordinal; the "true" differences between scale scores are unlikely to be so unequal that treating them as equal will be substantively misleading. The real problem is not so much the inequality of the true intervals as it is the loss of information about differences between people with the same score that comes as a result of having only a few different score values.

Whatever you do, don't use Spearman correlations (or anything else that converts the data to ranks and then uses the ranks as if they were on an interval scale), because that confounds the intervals between scale scores with the proportion of people having each score. Spearman correlations should be used only when there are few ties in the data, when the number of different scores is almost as big as the number of people.


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