Estimation of oblique structure via penalized likelihood factor analysis

TL;DR

This paper introduces a penalized likelihood factor analysis method that accounts for correlated factors, improving the estimation of sparse models especially when factors are not orthogonal.

Contribution

It proposes a novel maximum penalized likelihood approach incorporating factor correlation, addressing limitations of orthogonal models in correlated factor scenarios.

Findings

The method outperforms traditional orthogonal models in simulations.

It provides sparse solutions suitable for high-dimensional data.

Real data analysis demonstrates practical utility.

Abstract

We consider the problem of sparse estimation via a lasso-type penalized likelihood procedure in a factor analysis model. Typically, the model estimation is done under the assumption that the common factors are orthogonal (uncorrelated). However, the lasso-type penalization method based on the orthogonal model can often estimate a completely different model from that with the true factor structure when the common factors are correlated. In order to overcome this problem, we propose to incorporate a factor correlation into the model, and estimate the factor correlation along with parameters included in the orthogonal model by maximum penalized likelihood procedure. An entire solution path is computed by the EM algorithm with coordinate descent, which permits the application to a wide variety of convex and nonconvex penalties. The proposed method can provide sufficiently sparse solutions, and be applied to the data where the number of variables is larger than the number of observations. Monte Carlo simulations are conducted to investigate the effectiveness of our modeling strategies. The results show that the lasso-type penalization based on the orthogonal model cannot often approximate the true factor structure, whereas our approach performs well in various situations. The usefulness of the proposed procedure is also illustrated through the analysis of real data.