What to do with a variable that loads equally on two factors in a factor analysis?

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?
• What is your goal that you are using factor analysis to achieve? May 12, 2013 at 2:31
• 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). May 12, 2013 at 3:04

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.

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
• 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. May 12, 2013 at 5:56
• 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 . May 12, 2013 at 6:01
• Nice list of references! May 12, 2013 at 11:17