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I have a 40 item questionnaire (20 positive and 20 negatively phrased questions, 1-5 Likert scale), which has been taken by 363 people. Originally, the responses seemed to show two clear factor loadings, simply reflecting the positive and negative question phrasings (which i know is common).

However, I then discovered that the software I was using was not reverse-scoring the positive items as it should have been doing. The odd thing is that after adjusting the scores (so changing a 5 to a 1 and a 2 to a 4) for the relevant questions led to the removal of the loadings on question type...

Is this right? I was under the impression that the sign of factor loadings will flip based on whether you reverse reversed items, but the actual loadings would stay the same. This does not seem to be what is happening for my data...

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  • $\begingroup$ What happens when you truly just "flip" the scores in the sense of negating them (so that $5$ becomes $-5$, etc)? (This will reveal whether your analysis has centered the variables or not.) $\endgroup$ – whuber Jan 10 '17 at 17:01
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If you reversed all the items, then yes, the factor structure should be retained. But reversing only some of the items changes the relationship between items and hence the factor structure.

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  • $\begingroup$ Wouldn't it depend on how the reversal is coded and whether the values are centered? If they are centered at the mid-range, for instance, then reversal is a linear transformation (a negation), which merely changes the signs of some coefficients in the factor analysis. $\endgroup$ – whuber Jan 10 '17 at 17:30
  • $\begingroup$ @whuber I think you're right, but I can't check right now. $\endgroup$ – Kodiologist Jan 10 '17 at 18:44

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