For the modeling process, we will follow the following steps:
Extract the components and determine the number to retain
Rotate the retained components
Interpret the rotated solution
Create the factor scores
Use the scores as input variables for regression analysis
There are many different ways and packages to conduct PCA in R, including what seems to be the most commonly used prcomp()
and princomp()
functions in base R. However, for my money, it seems that the psych
package is the most flexible with the best options. For rotation with this package, you will also need to load GPArotation
.
To extract the components with the psych
package, you will use the principal()
function. The syntax will include the data (pca.df
) and number of the components to extract. We will try 5
, and we will state that we do not want to rotate the components at this time. You can choose not to specify nfactors
, but the output would be rather lengthy as it would produce k-1 components...