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I received the following question via email and thought it would be suited to this site:

I have a debate with a friend about factor loading and squared multiple correlation. ... In my debate with my colleague, I argue that regression weights/factor loading above 0.6 is enough for a construct. I mean for a construct which factor loading below 0.6 should be deleted because of the convergent validity problem. However, the colleague of mine argued that we also need to see squared multiple correlation. For squared multiple correlation below 0.7 we have to delete the items. So, now I am getting confused since in my research dataset, I found many items with squared multiple correlation below 0.7 but factor loading above 0.6. Should I delete these items?

So please advise me in your knowledge whether we really need to see squared-multiple-correlation or factor loading is enough?. In addition, actually what is the function/utility of squared-multiple-correlation. Is there a cut off value for squared-multiple-correlation?

Thus, I distil from this email a core question:

What decision rules should be used regarding squared multiple correlations and factor loadings when deciding on whether to retain an item of a question in the context of factor analysis?

Jeromy Anglim
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  • What sq. multiple correlation? Of each item as a linear model of all the other items - i.e. the _image_ value? In principal factoring method, this value is used as the starting value of the communality; and it is the only use of it. Except of in Image FA, Mult R seems not to be importance in selecting items. KMO is, but it is a bit a different thing. – ttnphns Aug 12 '13 at 07:15
  • Regarding the magnitude of loadings... I don't think there exist a theoretical threshold. Lower are the correlations, lower will be the loadings, but the factor structure can be no less valid if the correlations are reproduced well enough. And in fact, sometimes I may need to develop tight (homogeneous) factor validated scale and sometimes I may accept a loose one. After all, factor's items measure different facets of the trait's manifistation, the facets which need not to flourish [simultaneously](http://stats.stackexchange.com/a/31979/3277). – ttnphns Aug 12 '13 at 07:33
  • Depends also on the number of items. It makes a difference whether you have three or 15 items with loadings around .5. In the end, it's a question of reliability, isn't it. Maybe rules of thumb / cutoffs on reliabiltiy are more helpful then on loadings / squared multiple correlations? – hplieninger Aug 12 '13 at 08:55

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