Exploratory factor analysis - promax & factor cross-loadings I have a question regarding the best practice for dealing with cross-loadings on factors after conducting an exploratory factor analysis using a promax rotation. Just to give a bit of background information, I am trying to determine the factor structure of a set of 20 questions that I created about spirituality (based on PCA which identified 4 components). After conducting the EFA with 184 participants, I noticed that quite a few of the questions are cross-loading onto two or three factors. I read online that you should eliminate questions whose cross-loadings are less than or equal to .2, but I am confused because doesn't an oblique rotation (promax) imply that there is inter-correlation? For example, if question 2 loads onto factor 1 (.234), factor 2 (.346), and factor 3 (.212), what should I do?
 A: Firstly, principal components and factor analysis are quite different methods. PCA is normally used more as a data reduction technique, while factor analysis is more concerned with finding a latent structure.
On the cross loadings, the oblique rotation allows the factors to be correlated, but typically one would not want items to load on multiple factors. In this case, I would probably examine the factor loadings using other oblique rotations such as oblimin to see if these cross-loadings still appear. 
Cross loadings of below .3 are often ignored, but if you have multiple samples with the same cross-loadings, then this may be an indication that the item is indeed associated with more than one factor. Typically, these items are discarded, and I would probably do so unless you have a strong theoretical or practical rationale for retaining them.
Finally, it sounds like you have two samples. In this case, I would perform EFA on your first sample, and then use the second sample to validate your model. This will raise the probability that you are modelling something real, rather than noise. 
A: @Madeline, if, after various rotation and solutions, you find items consistently load (> 0.3) across major factors - you might consider the existence of a higher-order construct.  For example, an item assessing general well-being might cross-load on more specific factors associated with clarity of thought, social engagement, and existential purpose.  If you have several of these items (3 or more) you might use a hierarchical (higher order) factorial model, or simply pull them out and examine them using a separate run.  Factor analysis is intended as a structural validation tool not an interpretive tool (which is best left for other validation procedures). 
