I want to find out the relationship between 6 independent variable (4 categorical, 2 continuous) and 6 dependent variables (5 likert scale). As my data is categorical (likert scale) I thought of using logistic regression (i think ordinal), but I have to reduce my dependent variables for which I used principal component analysis (PCA) to reduce in two factors. But using PCA make my data type continuous as compared to original data that was categorical. My question is that
Could I now run simple regression on the 2 factors, means is it logically correct to change the data type (from categorical to continuous) and using regression instead of logistic regression? OR Do you have any other solution?