Dear friends,
Kindly clarify the following doubt.
The measurement model has 6 constructs (A, B, C, D, E, and F). A has 7 items, B has 6 items, C has 9 items, D has 5, and E has 12 items.
Now, on performing PCA with varimax rotation, one item from "B" showed cross loading (~.40) with construct "F" and one item from "D" cross-loaded with"A".
Nevertheless, loadings of items in original constructs (B and D) were comparatively higher (.50 and .61 ) than that of cross loads.
The constructs A, B, C, and D are exploratory in nature. The CMV of the model is found to be 26%.
I also sense that there is no theoretical resemblance in these cross-loaded items, however, there is a similarity in the wordings.
Should I incorporate these items into structural model( SEM in AMOS) or continue the analysis excluding these items.
Kindly suggest.
You can decide based on the following
. Cross loading occurs for all items, but the issue is to have clean loading {difference more than .20}.
. If the loading is above .40 and not clean, then you can choose either to delete the item or keep it under a factor based on the theoretical/logical meaning, you can decide this.
. You can try PCA with different type of rotation to get better solution.
. However, if the scale is already has a good psychometric properties in other studies, you can only start with CFA, if it remain stable with same original structure, then you can keep it as it is, regardless of EFA.
From what you say, I understand that items belonging to A, B, C, and D are new, not previously tested items, and therefore EFA should be preferred over CFA. Am I getting it right? If it were the case that these measures' factor structure had already been tested in a previous study, I'd suggest you use CFA over EFA. On the other hand, please consider the fact that PCA is not EFA, strictly speaking. If you're trying to develop a measurement model to be included in a future SEM model, it may make more sense to perform EFA instead of PCA.
Now, regarding your cross-loadings, if they make no theoretical sense but seem to be an spurious effect of wording, then the indicators' wording should be modified and tested again in a new sample. However, this is not always possible due to logistical reasons. Perhaps you can consider dropping these items, but please make sure that it does not affect content validity of your measure.
Thank you so much for your suggestion. I performed both EFA and PCA, the results doesn't vary significantly. I consider your opinion of dropping these cross loaded items. It does affect the content validity in terms of discriminant validity of one of the constructs. Nevertheless, I have no other way out other than mentioning the same as a limitation. Thanks again..!!
You can decide based on the following
. Cross loading occurs for all items, but the issue is to have clean loading {difference more than .20}.
. If the loading is above .40 and not clean, then you can choose either to delete the item or keep it under a factor based on the theoretical/logical meaning, you can decide this.
. You can try PCA with different type of rotation to get better solution.
. However, if the scale is already has a good psychometric properties in other studies, you can only start with CFA, if it remain stable with same original structure, then you can keep it as it is, regardless of EFA.
@Sayoni What do you mean exactly when you say that dropping the cross-loaded items would affect discriminant validity? Do you get an inflated correlation between your factor and another variable when you do that?
Thanks, Ahmad..a great information indeed... :) :)
@Pablo...yes..it did.. but I have come across few references which indicated that the correlation should below 0.85 (in a CFA model) to establish discriminant validity.
We have just published an article about scale purification, i.e. the process of eliminating items from multi-item scales. We discussed some parts of your question in our article. We have used the example of SCM, but our framework can be applied to any other discipline. Download: https://doi.org/10.1108/SCM-07-2016-0230 (or request via my ResearchGate page).
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