Alternative Penalty Functions for Penalized Likelihood Principal Components

The penalized likelihood principal component method of Park (2005) offers flexibility in the choice of the penalty function. This flexibility allows the method to be tailored to enhance interpretation in special cases. Of particular interest is a penalty function in the style of the Lasso that can be used to produce exactly zero loadings. Also of interest is a penalty function for cases in which interpretability is best represented by alignment with orthogonal subspaces, rather than with axis directions. In each case, a data example is presented.