# Principal component regression (PCR) with some of the original predictors left out of PCA

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?)

• I don't know of any studies using this technique, but I have used it myself in the past. I don't think there is any specific issue as long as no variables go into both the principal components and the regression itself. – eric_kernfeld Aug 23 '16 at 18:46
• The title seems a bit misleading because different variables are used in PCA and as original variables. However, I do not have a good alternative title proposal. – Richard Hardy Aug 23 '16 at 21:02
• @RichardHardy I tried editing the title. – amoeba Aug 23 '16 at 21:20
• @amoeba, looks better now, especially the text in bold! – Richard Hardy Aug 23 '16 at 21:24
• I would like to keep in their original form (i.e., not include them in the PCA with the other predictors) Please see my both above comments as irrelevant to the question in case you are speaking of "other predictors" which were not used in the PCA. I won't delete my comments, though. – ttnphns Aug 24 '16 at 14:15