Can I use construct/factor (revealed by EFA) mean scores as explanatory variables in a GLM (binomial family)?

Question

I have 11 motivations (M1-M11) in my questionnaire for ocean swimming. After running an EFA, I detected 4 underlying latent factors (relaxation, socialization, etc.) which explained about 58% of the variance.

1. Relaxation: M1,M2,M3
2. Socialization: M4,M6
3. Factor 3: M5,M7,M8
4. Factor 4:M9,M10,M11

Now, I am planning to model these motivations as independent variables to explain my binomial response variable (willingness to pay entry fee - yes/no), alongside other sociodemographic variables.

I am wondering if I should using the raw likert scores of each motivation as my explanatory variables, or use factor/construct mean likert scores. So either

response variable (yes/no) <- age+gender+education+M1+M2+M3+M4+M5+M6+M7+M8+M9+M10

OR

response variable (yes/no) <- age+gender+education+factor1 mean score+ factor2 mean score + factor3 mean score + factor4 mean score

whereby factor1 mean score == M1+M2+M3/3 = 5+3+4/3 = 4 and so on.

Just to add as well that after running both models, the results I get is rather similar anyway. In the first final model, M5 is marginally significant (p=0.052) while age is significant (p<0.05), but this swaps around for the second final model (the factor mean to which M5 belongs to becomes significant, while age becomes marginally significant).

Thank you very much!

Answer 1

I would say it depends on your end goal. First, if you don't do the grouping, theres a lot more parameters in your models to be estimated. A rule of thumb is to have at least 10 observations per parameter. If in your final analysis you are interested in only the larger groupings, then it might be worthwhile to only regress over the groupings. This is similar to a principal component regression model