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I have a panel dataset from a survey before and after an intervention. One question is a Q-method-style question where students have been sorting statements about the type of teaching they receive. In Q-method, you do an exploratory factor analysis where the respondents are considered the items (they are the ones who are "loading" on the factors).

I can do a factor analysis on the pre- and post-intervention datasets by themselves, or on the compiled dataset (but that introduces dependent observations, which breaks the assumption of independence). In the post-intervention analysis I get a more clear picture of a desirable practice in one of the factors. So I want to understand how many of the students who got the intervention, moved from one of the other practices, to this new practice - compared with the control group.

So I want to use the results from the post-intervention factor analysis as an outset for analysis of the pre-inteventions data.

In ordinary factor analysis that would equal having the same respondents answering two sets of items, and letting the factor loadings of the first set determine the factor loadings of the second set by looking at the responses of both set one and two.

I have looked at the factor analysis model, but I am not able to figure out how I do this.

I am using R in my analysis.

jeppeb
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  • "In ordinary factor analysis ... letting the factor loadings of the first set determine the factor loadings of the second set by looking at the responses of both set one and two" Can elaborate on this? And do you have a concrete approach how to do it? – ttnphns Aug 24 '22 at 16:59
  • Suppose I have 10 items, and do a factor analysis on responses from respondents. Two factors turn out to make sense. Now I introduce 10 more items and make the same respondents answer these 10 items. I want to find out how the new items load on the two existing factors. I can run an analysis on all 20 items, but that will result in two (or more) new factors. So I need to fix the item loadings from the first analysis and find a solution for the second set. Does that make sense? – jeppeb Aug 26 '22 at 08:37
  • In FA, unlike PCA, the correlation (loading) between a hold-out variable and the factor is not uniquely determined. Suppose you have variables X, Y, Z, and you performed FA on X, Y and extracted factor F. The correlation between F and Z is not unique value, it can vary in some range. The reason why it is so is that F does not lie in the space of X,Y. But with PCA, it is different: the pr. component P lies in that space, and so correlation P-Z is a unique value. – ttnphns Aug 26 '22 at 10:27
  • What you are actuly asking is "can I perform FA holding some variables passive (aka supplementary)".My answer above was "it is problematic in FA". – ttnphns Aug 26 '22 at 10:59
  • The problem is palliatively solved if you compute factor scores of F. (Then compute the correlation between them and Z.) I said "palliative" because factor scores - unlike pr. component scores - are not uniquely determined themselves - they just are approximations – ttnphns Aug 26 '22 at 11:09

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