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I am running exploratory factor analysis and have extracted 3 factors, with items clearly loading on each one.
However, it appears to me that the items that have loaded onto the first factor could be further split into two, theoretically meaningful, groups. My question is therefore, could I re-run factor analysis on the first factor only to derive two groups Factor 1a and Factor 1b?

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  • $\begingroup$ George, doing separate FA on a subset of items just means that you arbitrarily throw away the rest items, the items that you initially collected because they correlate and because they cover the field where latents grow. You chuck out them as if they were irrelevant. You may do it, but think twice. Think of the consequences. $\endgroup$ – ttnphns Feb 19 '14 at 16:59
  • $\begingroup$ Also, please do not say "item loads onto a factor". More correct is "factor loads onto an item": loading is the regression coef. in predicting items by factors, not vice versa. $\endgroup$ – ttnphns Feb 19 '14 at 17:01
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You need to elaborate your question a bit. It all depends on what actually do you want to do with these factors. Is it just interpretation, or is it something else. In any case you should think over these points first

  1. How did you decide upon the initial number of factors (which in your case is 3), was it the scree plot that you got from eigen values.?
  2. What is the criteria which is leading you to decide that factor 1 should be splitted into further sub factors. As far as I understand the latent factors that you extract in the first run explain the maximum variance.

Solution

  1. You should try to extract that additional factor in the first run itself by manually setting the number of factors to 4 rather than taking it from the scree plot.
  2. If it all you want to split into sub factors then, that problem will be different from the original problem , but there is no harm in doing it.

My View : If we were able to club the variables into latent factors by looking itself only, then there was no need of factor analysis at the second stage at all

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  • $\begingroup$ Based on eigen values, I initially extracted 5 factors, however there was a lot of cross-loading of items across all of these factors. A scree plot indicated that 3 factors would be the optimal solution, so I re-run the analysis on 3 factors only. $\endgroup$ – George Feb 19 '14 at 12:02
  • $\begingroup$ Great ,Do those 3 factors make sense to you ? Also i will reiterate if it appears to you that factor 1 can be sudivided into 2 factors then you already have done factor analysis in your mind. Above all its all about what you name those factors, statistically whatever you could extract, you already have achieved that in the first run itself $\endgroup$ – NG_21 Feb 19 '14 at 12:08
  • $\begingroup$ Additionally, in regards to the criteria that i'm using to decide that there could be a sub-factor - well, it is based on a pre-conception I suppose informed by the findings of a similar study. I am hoping to derive groupings (originating from a likert survey of people's reactions to their local environment) that can be used as a response variable in relation to an experimentally manipulated scenario. $\endgroup$ – George Feb 19 '14 at 12:09

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