Dear Prachi Sanghvi

in short: this is not done. You would want your items to load onto one factor and one factor only.

Best

Marcel

I agree with Marcel.

Hello Prachi,

If factors are correlated more than a little, then cross-loadings can and will be observed (note that I am talking about variable-factor loadings/correlations, not the factor pattern matrix, which outlines emphasis given to variables in the identification of a factor). So, the first question for me is, are your factors correlated, and if so, by more than a little?

Interpretation of factors can indeed be easier when variables load on one and only one factor (as in Thurstone's idealized "simple structure" solution). If you embrace that ideal, then you must be prepared to jettison variables which don't conform to the intended pattern. However, there are several personality measures that include multiple items/questions/stimuli with salient loadings on multiple factors, and these measures still offer utility.

You're perfectly free to set the condition that no cross-loadings are allowed in your solution; but there's nothing about the basic factor model that prevents you from having cross-loadings.

Good luck with your work.

Prachi Sanghvi, in my view, it's a bit difficult to provide you with advice because you've provided too little information.

One important element is whether you are referring to cross loadings in a pattern matrix following an oblique rotation. Another important element is the extent to which the cross loadings occur; cross loadings with a difference < .20 could raise concern, and with a difference < .10 even more concern. Another important element is exactly how many cross loadings there are on exactly how many factors.

Still another element is which rotation you are applying to your data. Even within either orthogonal or oblique rotations, there is some opportunity for choice of rotation - and some rotations, with some data sets, produce cleaner factor separation than do others. Have you tried different rotations?

Also, have you engaged in some iterative steps by deleting items that did not load on any factors and items that had very close cross loadings?

Once some of that information is available, it is likely to be much easier to help you.

All that aside, I think that having items that belong to more than one factor creates conceptual muddiness.

We can often handle multidimensionality fairly easily in an SEM framework (by estimating correlated errors, modeling additional factors, etc.), if we have to do so. However, when designing an instrument, multidimensionality is not ideal because it violates our goal of simple structure (as David Morse mentioned above); it can also cause problems when you go to calculate statistics like coefficient alpha, which assumes unidimensionality. The inclusion of cross-loading items may result in inaccurate estimates of alpha.