Mark D. Newmeyer, I can fully appreciate why you've asked your question.

As I understand it, factor analysis can be performed on dichotomous data by using polychoric correlations. I'm sure there will be sites on the web that would be helpful, but you might also need a tame statistician to help you.

Hello Mark

if you use Mplus or R/lavaan, you can handle binary indicators by respective estimators (e.g., DWLS, WLSMV), see e.g., https://lavaan.ugent.be/tutorial/cat.html

Best,

Holger

Hi Mark

As usual Robert and Holger have provided great answers, and their approaches are based on the idea that the binary variable is a crude indicator of a continuous underlying variable. You might want to treat the scores as truly categorical and this would bring Item response Theory models into the frame. It's an exciting time as the boundaries between these seemingly different psychometric models (FA/IRT) are now pretty faint.

Mark

Thanks for these responses. I'm not a true statistician, but can puzzle through most things (well until it gets to complicated matrices math). The polychoric correlations conceptually make sense. Thanks Robert and Holger for your responses and pointing me in the right direction. I'm tempted to figure this out in R and run the analysis and compare it to what I would get in SPSS if I just ran an exploratory principal component. Always more to learn : )

Mark D. Newmeyer--to add to Robert Trevethan's comments, here is a resource from IDRE, which generally describes the process for generating a polychoric correlation matrix and conducting a factor analysis:

https://stats.idre.ucla.edu/stata/faq/how-can-i-perform-a-factor-analysis-with-categorical-or-categorical-and-continuous-variables/

This resource is geared toward STATA, but the general principles hold.

~Sarah

Mark D. Newmeyer - here is an applied example that touches on all the points others already made: Conference Paper Assessing the Dimensionality of the Test of Ethical Reasonin...

Thanks Bozhidar. Look forward to reading the article.