I have a dataset that is used to predict birth weights of babies. I have completed PCA on the parents attributes and have used that as one new combined PCA variable ParentsAttributes. I am using this column plus other original attributes related to the baby to predict it's birthweight.
My question is, is the above a correct approach or if I am using PCA should I use it on all variables?
Let's say you have 4 parental attributes that measures height, weight, blood pressure and cholesterol levels. Chances are, some of those items are going to be highly correlated. Height and weight is an example.
If you try to put all 4 those variables into a regression model at the same time, the model might tell you that both the weight and height of the parents are good predictors of their child's birth weight, but because they overlap/correlate so much themselves, the model can't tell which one of them is actually responsible for predicting the child's birth weight. This is usually referred to as collinearity. The more predicator/independent variables you throw at your regression model, the worse this problem tends to become.
One way around this is to do a PCA, which will take those 4 parental characteristics and reduce them to "components" which are sort of like combinations or groups of the original 4 variables that fit together from a statistical point of view. So instead of having to deal with height and weight separately, which is messing with your model, you now hopefully get a "component" that combined height and weight into a new variable that you can think of as representing "parent size". Another component that combined blood pressure and cholesterol levels maybe represents "cardiovascular health". You can now use these components as predictor/independent variables in your regression model to predict child birth weight and because the PCA procedure got rid of most of the collinearity by combining variables that go together, you should be good to go. Just be careful, as it changes the interpretation of your regression model slightly.
Now, to answer your question. Whether or not you include variables in the PCA or not depends entirely on what it is you are trying to do, but you don't HAVE to, no. If you have a questionnaire that specifically measures parental attributes, then it would not really make sense to chuck completely unrelated variables such as "number of gynecologist visits" or "baby genetic markers" into a PCA alongside the parental attribute items.
