Cross loadings is simply items that loads on two (or more) factors, i.e., on another factor than they were suppose to load on. You will see it in your modification indices. The fit of your model will not be optimal. You should probably remove such items from your model.

Best

John Kåre

Using the assessment of cross-loadings, once the correlation between each item and other constructs became weak, discriminant validity was determined to exist (Gefen and Straub, 2005, p. 92). In other words each items was only correlated to one construct which it was theoretically belong to. This approach somehow is similar to the process of assessment of loading factor in exploratory factor analysis . In this way, the table of cross loading was prepared and it showed all indicator loadings value were greater than all of its cross loading values.

Hello Hasfi,

I would not disagree with the previous comments. However, there may be a couple of other areas to consider in your situation.

(1) You might find that covarying observed items across first-order factors may be helpful … BUT only when there is reason to do so (beyond mod indices). This may include similar wording, order-bias, etc. Or they may be related theoretically to some common third factor (i.e., method factor).

(2) Some have questioned the inherent assumption that cross-loadings between items and non-target factors are exactly zero (for a CFA). Others have noted that indicators rarely, if ever, perfectly and uniquely relate to a single construct and will almost always display some degree of construct relevant association with nontarget factors assessing related or especially hierarchical constructs, as seems to be the case for you. This has led to more recent interest in bi-factor analysis, and bifactor-ESEM. This may be of some interest to you.

Here are a couple of references to get you started:

Howard, J. L., Gagne, M., Morin, A. J. S., & Forest, J. (in press). Using Bifactor Exploratory Structural Equation Modeling to Test for a Continuum Structure of Motivation. Journal of Management.

Morin, A. J. S., Arens, A. K., & Marsh, H. W. (2016). A Bifactor Exploratory Structural Equation Modeling Framework for the Identification of Distinct Sources of Construct-Relevant Psychometric Multidimensionality. Structural Equation Modeling: A Multidisciplinary Journal, 1-24. doi:10.1080/10705511.2014.961800