# Use of further analysis on factors formed by principal component analysis in regression

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?

## 1 Answer

When you did ordinary (linear) PCA on your likert-scale variables you already treated those variables as scale, or continuous, variables (variables with evenly spaced measuring benchmarks). To put in other words, you haven't regarded them as ordinal so far.

To recognize their ordinal (i.e. potentially not evenly spaced) nature you might consider to perform categorical PCA (CATPCA) which quantifies measuring levels nonlinearly to achieve the "best" principal components.

And yes, principal components are continuous, so usual regression is apt to them.

• Thanks for the reply. Could you please tell me which regression (linear/ordinal/logistic) could I run after having factors from CATPCA? – wxa Jan 10 '12 at 1:30
• Linear: Principal components after CATPCA are also continuous. It is input variables to CATPCA - they need not be continuous. – ttnphns Jan 10 '12 at 3:08
• @ttnphns-Thanks it is a great help. please just confirm that whether I should use the object scores (2 dimension) in regression? and if it is 2 dimensions, then each will be run separately for regression? – wxa Jan 10 '12 at 3:48
• Yes, exactly. Note also, that to use your Likert variables in CATPCA they should be coded 1,2,3,..., no other way. (Still, I cant't help wondering why you needed data reduction - such as PCA - of variables that you plan to be dependent in regression; what could be rationale for that?) – ttnphns Jan 11 '12 at 11:20
• @ttnphns- I have to reduce dependent variables in SPSS as e.g my DV is business development and for it I asked 8 likert scale questions such as increase in sales, profit, size, labour.....If I will not reduce it, it means there is eight models of increase in sales, profit, size....and no model of business development. – wxa Jan 14 '12 at 0:02