Simultaneous variable and factor selection via sparse group lasso in factor analysis

ABSTRACT

This paper considers variable and factor selection in factor analysis. We treat the factor loadings for each observable variable as a group, and introduce a weighted sparse group lasso penalty to the complete log-likelihood. The proposal simultaneously selects observable variables and latent factors of a factor analysis model in a data-driven fashion; it produces a more flexible and sparse factor loading structure than existing methods. For parameter estimation, we derive an expectation-maximization algorithm that optimizes the penalized log-likelihood. The tuning parameters of the procedure are selected by a likelihood cross-validation criterion that yields satisfactory results in various simulation settings. Simulation results reveal that the proposed method can better identify the possibly sparse structure of the true factor loading matrix with higher estimation accuracy than existing methods. A real data example is also presented to demonstrate its performance in practice.

KEYWORDS:

• Expectation-maximization
• factor analysis
• factor selection
• likelihood cross-validation
• penalized log-likelihood
• sparse group lasso
• variable selection

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62H25
• 62P15

Acknowledgements

We would like to thank the three anonymous reviewers for their valuable feedback that helped improve our original manuscript significantly.

Disclosure statement

No potential conflict of interest was reported by the authors.