分野別セミナー

The factor analysis model has been widely used to explore the covariance structure by the construction of (unobserved) latent factors. A traditional estimation procedure in use is the following two-step approach: the model is estimated through the maximum likelihood method, and then a rotation technique is utilized to find interpretable factor loadings. On the other hand, the penalized likelihood procedure has been recently developed as an alternative to rotation techniques. We show that the penalized maximum likelihood procedure can be viewed as a generalization of the traditional two-step approach, and can produce sparser solutions than the rotation technique. We introduce various penalties used for penalized maximum likelihood factor analysis: lasso, minimax concave penalty, and the product-based elastic net. Real data analyses are presented to illustrate the usefulness of the penalized maximum likelihood estimation procedure.