I recently gave a free webinar on Principal Component Analysis. We had almost 300 researchers attend and didn’t get through all the questions. This is part of a series of answers to those questions.
If you missed it, you can get the webinar recording here.
Question: In Principal Component Analysis, can loadings be both positive and negative?
Recall that in PCA, we are creating one index variable (or a few) from a set of variables. You can think of this index variable as a weighted average of the original variables.
The loadings are the weights.
The goal of the PCA is to come up with optimal weights. “Optimal” means we’re capturing as much information in the original variables as possible, based on the correlations among those variables.
So if all the variables in a component are positively correlated with each other, all the loadings will be positive.
But if there are some negative correlations among the variables, some of the loadings will be negative too.
Here’s a simple example that we used in the webinar. [Read more…] about In Principal Component Analysis, Can Loadings Be Negative?