# Estimation of oblique structure via penalized likelihood factor analysis

arXiv: https://arxiv.org/abs/1302.5475 · HTML: https://mlsanity.com/paper/1302.5475/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2013.

## Built on by (most cited first, 1 of 1)

- [Identification of Nonlinear and Dependent Latent Factor Structure through Clique Search](https://mlsanity.com/paper/2609.32926/) (2026)

## Abstract (arXiv)

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.