Hello,

I will attempt to address and answer your question; however, I tend to ramble so I may include some irrelevant details.

First, why is it that you can only include 10 independent variables? Are you basing this off of power calculations and following the usual suggestion of variable number=10*k/p where k=number of covariates and p=proportion of ‘positive’ cases within the population of interest? (Peduzzi et al., 1996). If this is the case, it should be noted that the 10 events per independent variable ‘rule of thumb’ is considered by many to lack theoretical support as it is strictly based off of simulation studies. To clarify, even when there are only 2-4 events per independent variables the resulting logistic model often still provides acceptable results (Vittinghoff & McCulloch, 2007).

Unless there is a very specific reason as to why you cannot use more than 10 independent variables, this decision seems rather arbitrary. It is true, we strive for the most parsimonious model possible and having too many IVs leads to overfitting which produces ridiculous estimates and leads to model that ends up only being predictive of the utilized dataset (Hosmer et al., 2013). However (as you probably know), within generalized linear models, such as binary logistic regression, it is assumed the models have all relevant IVs included, no irrelevant IVs included, and the relationship of these IVs are linear to the DV (Mendard, 1995).

-          With this being said, if you had 30 variables included in your model and: 1) these 30 variables did not possess any glaring existence of collinearity (or other variable assumption violations); 2) the resulting coefficient estimates and standard errors were not absurd values; 3) the statistical analyses of model fit supported the more vs. less variable number; 4) there was a theoretical reason for each of these variables to be included – then I would say this is a better model than one with a third as many variables. IT SHOULD BE NOTED however, I am making a bunch of presuppositions and I am not saying that your specific scenario needs to have more than 10 variables but hypothetically it would be possible.

With that being said, you probably already have your mind set on using only 10 independent variables, which is fine. To now specifically address your question:

you want to know if, upon using factor analysis to reduce the 30 IVs into factor clusters, whether or not these factors are suitable for the new IVs within your logistic regression.

Essentially, there is nothing wrong with doing this – the majority of quantitative scales (i.e., Quality of life, various psychometrics instruments, etc.) have used factor analysis in some form to derive the subscales of these various instruments. Point being, these subscales, which are the result of factor analysis, are well accepted IVs within generalized linear models.

-          With this being said, you need to make sure your factor analysis is done correctly and the resulting factors make both numerical sense but more importantly theoretical sense.

I realize I say too much; hopefully this response is helpful and feel free to ask me to clarify or further elucidate anything I have presented here.

Wishing you the best,

Logan Netzer

References:

Hosmer DW, Lemeshow S, Sturdivant RX. (2013). Applied logistic regression. Third Edition. New Jersey; John Wiley & Sons.

Menard S. (1995). Applied Logistic Regression Analysis. Sage University Paper series on Quantitative Applications in the Social Sciences, 07-106. Thousand Oaks, CA: Sage.

Peduzzi P, Concato J, Kemper E, Holford TR, Feinstein AR. (1996). A simulation study of the number of events per variable in logistic regression analysis. Journal of Clinical Epidemiology 49:1373-1379.

Vittinghoff E, McCulloch CE. (2007). Relaxing the rule of ten events per variable in logistic and cox regression. American Journal of Epidemiology 165(6):710-718.

Many thanks Sofia and Logan for your time. That is really helpful.