10.4 Principal Components Analysis (PCA)
Each of the above two techniques involves eliminating variables that have small--although possibly still significant--effects on a dependent variable. Wouldn't it be nice if we could keep all of the benefits of these "less-important" variables without actually deleting them? Yes it would. Therefore, it's sometimes preferred to actually transform your larger number of variables into a smaller set of more independent variables. In other words, you can still use every one of the 17 variables you may start with, but combine six of them into into one, another three into another one, and the last eight into another one resulting in three total variables. However, you aren't simply averaging those variables together. Some ar more important than others. And how do you decide which of the original variables go into which of the newly generated variables? We'll use principles components analysis (PCA) to accomplish this:
Here's another example using survey-based research that is a better adaptation of PCA: