Modeling and evaluation

For the modeling process, we will follow the following steps:

1. Extract the components and determine the number to retain.
2. Rotate the retained components.
3. Interpret the rotated solution.
4. Create the factor scores.
5. Use the scores as input variables for regression analysis and evaluate the performance on the test data.

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.

Component extraction

To extract the components with the psych package, you will use the principal() function. The syntax will include the data and whether or not we want to rotate the components at this time:

> pca <- principal(train.scale, rotate="none")

You can examine the components by calling the pca object that we created. However, my primary intent is to determine what should be the number of components...