Sparse estimation via nonconcave penalized likelihood in a factor analysis model

We consider the problem of sparse estimation in a factor analysis model. A penalized likelihood procedure that imposes a nonconvex penalty on the factor loadings is presented. In order to compute the entire solution path, a new efficient algorithm via the EM algorithm along with coordinate descent is proposed. Our algorithm can be applied to a wide variety of convex and nonconvex penalties. Furthermore, the proposed procedure allows us to analyze high-dimensional data such as gene expression data. We introduce a new graphical tool that outputs path diagram, goodness-of-fit indices, and model selection criteria. The graphical tool is helpful in finding a suitable value of the regularization parameter. Monte Carlo simulations are conducted to investigate the performance of the proposed modeling strategy. Two real data examples are also given to illustrate our procedure.