I have a data set from an opinion survey with many variables, and to conduct regression analysis I would like to reduce the number of variables; because curently I actually have more variables than responses. I've tried principal component analysis(PCA)/exploratory factor analysis(EFA), but I find it difficult to "interpret" the different factors. However, I think one can group the variables well based on theoretical considerations alone, so I thought confirmatory factor analysis (CFA) might be an option.
Unfortunately most resources on data reduction techniques point me to PCA/EFA. Does anybody know any resources that explain the process with CFA?
Alterantively, can anybody help me with the following more specific questions?
1) If my sole purpose of is to use the factor scores in regression analysis, do i have to worry about the fit statistics of the CFA at all? It seems to me that all I need are the factor scores.
2) As far as I understand, one can either constrain the variance or set set one of the variables in each of the groups to 1, again for my purpose of data reduction, does it matter which approach I use? Does the choice affect my factor scores? Or more specifically does setting one factor loading in each factor to 1 the comparison across factor scores?
3) I am struggling with the actual computational step going from the CFA results to the factor scores. I was using the Lavaan package in R, and can't seem to get the factor scores. or do i have to calculate the manually using the loadings? Does anybody know how this is done, or can reccomend a different package? (I realise this is a more a programming question than a conceptual qustion, but thought I'll add it nonetheless, hoping that somebody who might know about CFA in theory also has practical experience with it in R)
Thanks in advance!
NB: In case anybody is alaremd by the statement about the relatively sample size above. I don't really care so much about inference here, as my sample is pretty much the entire population. NB2: I am planing to use the factors only on the right-had side of the regression. The left-hand side variable comes from elsewhere.