How to interpret the factors in factor analysis




In Factor Analysis,we aim to get some variables not in the data(factors) which explain the other variables that are present.
How are these factors then interpreted.For example say I do a factor analysis on a dataset having 500 variables and end up with 8 factors which explains the maximum variance in the data.
How are these then interpreted?Do we use these factors (say in a linear regression) in place of the variables.
If yes then how do we interpret the results?


Factor analysis and Principal component are both used in variable reduction. One way is to use them directly in your regression model, as you suggested. This makes sure that there is zero multicollinarity in the model. However, in most cases we try to see factor loading to choose a variable which can serve as a proxy to this factor. Then we use that variable in the model. This does not make multicollinearity zero but helps to create a decent model (with low VIF).

Hope this helps,