Unscripted E4: Exploratory & Confirmatory Factor Analysis

Dan and Patrick introduce the basics of factor analysis, both exploratory and confirmatory, and describe potential advantages and disadvantages to each. They begin by discussing traditional factor analytic methods and then explore more recent developments in measurement and scoring. The conclude with how these methods might be best used in practice and make recommendations for further training.
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[@fredrickboholst]

I read somewhere that if you had terminal illness and wanted to stretch the remaining time in your life, you should spend it in a stat class! But time in your presentations flew so fast!!!! You had me at regression!

[@centerstat]

ha! I'll remember that one -- the corollary is that a stats lecture is a fail-safe treatment for insomnia. Thanks for the note -- I hope you find this silliness in some way helpful -- Patrick

[@fredrickboholst]

@@centerstat . . . the silliness!!! an indispensable spontaneity needed for topics like this. Well, your videos...watching them is my guilty pleasure. Especially because I do it during office hours! Hahaha. I do have fun watching you guys. ok, of course I learn growth curve modeling along the way. Seriously, both of you are a student's dream stat professors. I wish I had you in grad school. More power to you.

[@peterm3989]

I think Grice (2001) in Psych Methods also discusses the issue of factor score indeterminacy

[@louiebrown1]

Great video, thanks! I'm experienced in EFA (via SPSS) but new to CFA and am trying to establish the best approach (& software) for doing CFA with large sample non-normal data (from a likert-type scale). Non-normality is expected in data from my field. I was hoping I could use AMOS but am not sure AMOS will allow me to undertake modelling that is robust to non-normality. Would you mind pointing me in the right direction please? And/or suggesting a couple of good references for me to expand my understanding? Many thanks, Cynthia

[@centerstat]

Hi -- thanks for the kind words. Briefly, there are two issues to consider: do your items have a sufficient number of response options to be considered continuous, but remains non-normal; or do you have so few response options that the linearity assumption no longer holds and you must move to a nonlinear model. If the former, there are many good options using robust maximum likelihood; if the latter, you have to adopt an alternative estimator to the typical normal theory ML. One option is based on polychoric correlations and uses some form of weighted least squares estimation; another option is to use an ML estimator that is based directly on the discrete item responses. As of now, Amos provides neither of these options but uses a Bayesian approach instead. Different packages offer different options (e.g., lavaan, LISREL, and Mplus) each of which have certain advantages and disadvantages. A couple of citations and a podcast episode are below. I hope this is of some use -- Patrick quantitudepod.org/s2e27-reconnecting-with-discrete-data/ Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9, 466-491. Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17, 354-373. Savalei, V., & Rhemtulla, M. (2013). The performance of robust test statistics with categorical data. British Journal of Mathematical and Statistical Psychology, 66, 201-223.

[@louiebrown1]

@@centerstat Patrick, Thank you so much for your reply. I've worked through the 2 issues, your suggestions and references. These were very insightful! My likert style scale has 6 options and based on my reading can be considered continuous, and non-normality remains, so at this stage I'm intending to use Mplus with Robust ML. I'll be most interested to see how well the model fits! Thank you for your generous and detailed response. It really helped me to navigate what felt like a a minefield!

[@centerstat]

@@louiebrown1 Thanks for your very kind note -- I'm glad I could be of even trivial use. Good luck with your work -- Patrick