I just recently started learning about principal component regression (PCR) and I'm wondering if it's possible to use both principal components and original variables as predictors of a given outcome (the outcome is binary, so I'll need to perform a logistic regression). I have 34 predictor variables about perceptions of weather conditions, frequency and importance of land use and sea ice use, and land/sea ice travel behaviors and special travel equipment; given the large number of variables and strong correlations between certain variables, I'd like to run a PCA as a dimensionality reduction technique and aid with potential problems arising from multicollinearity.
However, I also have a few sociodemographic predictor variables that I would like to keep in their original form (i.e., not include them in the PCA with the other predictors).
Are there any problems with running a (logistic) regression analysis using both principal components and original variables as predictors? And, if this approach is alright, does anyone know of any studies/references using this approach?
(Also, I am technically running a categorical/non-linear PCA in SPSS (CATPCA), but I'm assuming the answer to my question is the same regardless of whether a linear or non-linear PCA is being performed?)