# Confirmatory factor analysis for data reduction (prior to regression)

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)

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.

• I would look into partial least squares for this type of problem. I wrote about PLS on my blog – Peter Flom Mar 25 '14 at 17:07
• Thanks, @PeterFlom! Good idea. I'll give that a try. Am I correct that PLS is more data-driven, i.e. more similar to PCA, than theory driven like CFA? – John Mar 25 '14 at 18:34
• I'd still be curious to hear any thoughts about my original question, on whether/how CFA can be used for data reduction. Would anybody have any pointers? – John Mar 27 '14 at 20:10

It's my understanding that EFA and CFA are essentially very similar, but differ in whether a solid theoretical foundation or researcher's arguments for a set of factors that is related to studied phenomena. Being a beginner and planning to perform EFA, CFA and SEM analyses for my dissertation, I collected a lot of resources. Below I will share some of them, which I think are relevant to your question.

1. http://www.jvank.nl/PP/down/BeamerFASEM.pdf (The best presentation on EFA that I've seen so far! I just love the detective/judge analogy!) Unfortunately, CFA explanation in this document is not comprehensive. The following slides do a better job at that and complement the first set of slides: http://people.ucsc.edu/~zurbrigg/psy214b/09SEM6a.pdf;
2. http://courses.ttu.edu/isqs6348-westfall/images/6348/Exploratory_Factor_Analysis_in_R.pdf;
3. http://www.statpower.net/Content/312/R%20Stuff/Exploratory%20Factor%20Analysis%20with%20R.pdf;
4. http://jeromyanglim.blogspot.com/2009/10/factor-analysis-in-r.html;
5. Resources on James Gaskin's StatWiki: http://statwiki.kolobkreations.com/wiki/Exploratory_Factor_Analysis, http://statwiki.kolobkreations.com/wiki/Confirmatory_Factor_Analysis;
6. James Gaskin's YouTube channel: https://www.youtube.com/watch?v=X-O-OcJPCe8 (This is just for EFA, check other videos in his SEM Series there);
7. https://personality-project.org/r/#factoranal;
8. http://tgmstat.wordpress.com/2014/01/15/computing-and-visualizing-lda-in-r (Dimension reduction using PCA and (!) LDA);
9. Somewhat "unusual", top-down method, called Bass-Ackwards technique: http://projects.ori.org/lrg/PDFs_papers/Goldberg_2006_BassAckwards_JRP.pdf (description), http://blogs.scientificamerican.com/beautiful-minds/2013/11/25/openness-to-experience-and-creative-achievement (example of application);
10. On selection of estimators for CFA: http://redfame.com/journal/index.php/ijsss/article/viewFile/27/29;
11. http://www.r-bloggers.com/structural-equation-modeling-separating-the-general-from-the-specific-part-ii (CFA)
12. 'qgraph' R package for PCA/EFA/CFA/SEM analysis and visualization: http://sachaepskamp.com/qgraph (details), http://www.jstatsoft.org/v48/i04/paper (more details);
13. 'semPlot' R package for SEM visualization: http://sachaepskamp.com/semPlot
14. CFA and SEM can also be performed by using 'plspm' R package. Details on PLS-PM and some other PLS-based CFA methods are available in free book by plspm's author Gaston Sanchez: http://gastonsanchez.com/PLS_Path_Modeling_with_R.pdf;
15. A nice book, integrating various multivariate techniques into a coherent description. After reading "inside", I concluded that it should be good for a beginner like me. I went ahead and ordered it - looking forward to learning from this book: http://www.amazon.com/The-Essence-Multivariate-Thinking-Applications/dp/041587372X.

I might update this answer with other materials I will run across. Hope it helps!