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After performing a factor analysis on a set of variables, I have one variable that loads equally on two factors.

  • What should I do with this variable that loads equally on two factors?
  • Should I remove this variable from the factor analysis, and rerun the factor analysis?
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  • $\begingroup$ What is your goal that you are using factor analysis to achieve? $\endgroup$
    – Jeromy Anglim
    Commented May 12, 2013 at 2:31
  • $\begingroup$ My study is cross-cultural research, based on Semantic Differential technique. I want to extract factors and compare results for two groups of students (first group from China, second group from Russia). $\endgroup$
    – drobnbobn
    Commented May 12, 2013 at 3:04

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Using factor analysis for scale construction is a bit of an art. It is common to drop items that load to a substantial degree on more than one factor after factor rotation.

That said, a few alternative ideas:

  • Consider whether you have extracted enough factors. Sometimes when you extract more factors cross-loading items or items that don't load much at all can load cleanly on one factor.
  • If this is only the initial phase of data collection and you are planning on generating more items, or you already have a large item pool, then it makes more sense to drop cross loading items. If this is a single shot, then you might be more reluctant to drop items.
  • You also need to consider what your threshold is for cross-loadings (.3, .4, .5). If you set it too high, then you might fail to identify problematic items. If you set it too low, then you may pick up cross-loadings that either reflect a little noise in the data or are more generally not going to substantively effect the purity of your factors.
  • Don't forget to think. Think about why the items are cross-loading. What is it about the two factors and the nature of the items that is leading to this cross-loading. There may be theoretical or other reasons why you want to model and retain cross-loading items.

References

You may want to read some of the following articles about factor analysis and scale construction:

  • Clark and Watson's Constructing Validity: Basic Issues in Objective Scale Development. PDF
  • Gerbing and Anderson's An Updated Paradigm for Scale Development Incorporating Unidimensionality and Its Assessment PDF
  • Reise, Waller, and Comrey's Factor Analysis and Scale Revision PDF
  • Hinkin's A Review of Scale Development Practices in the Study of Organizations PDF
  • Ford, MacCallum, and Tait's The Application of Exploratory Factor Analysis in Applied Psychology: A Critical Review and Analysis
  • Fabrigar, Wegener, MacCallum, and Strahan's Evaluating the Use of Exploratory Factor Analysis in Psychological Research
  • Costello and Osborne's Best Practices in Exploratory Factor Analysis: Four Recommendations for Getting the Most From Your Data Analysis
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  • $\begingroup$ Agree with all your points. However, the OP has revealed that their goal is not scale construction but cross-cultural comparison. In this context dropping a complex (cross-loaded, hence multisemantic) item will rather impoverish the analysis. $\endgroup$
    – ttnphns
    Commented May 12, 2013 at 5:56
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    $\begingroup$ Good point. I tweaked one of my dot points to make it clearer that you need to think. And that there may be theoretical reasons for wanting to retain cross-loaded items. That said, I imagine more needs to be known. A phenomena may be cross-cultural, yet you may still want to extract pure measures of the core cultural dimensions . $\endgroup$
    – Jeromy Anglim
    Commented May 12, 2013 at 6:01
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    $\begingroup$ Nice list of references! $\endgroup$
    – Peter Flom
    Commented May 12, 2013 at 11:17

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