Robust L1-norm Estimation for Exploratory Factor Analysis Model

Factor Analysis is a statistical technique used to understand the underlying structure of complex datasets by identifying latent variables that explain the correlations among multiple variables. Traditional factor analysis methods are often sensitive to outliers and noise, leading to unreliable estimates. So robust factor analysis is crucial for accurately identifying latent variables in datasets that include significant noise and outliers. Minimum Covariance Determinant (MCD) was widely used for robust factor analysis. The MCD estimator provides a robust estimate of the covariance matrix by minimizing the determinant of the covariance over a subset of the data effectively reducing the influence of outliers. In this paper, we propose a novel robust factor analysis method using L1-norm Exploratory Factor Analysis (L₁-norm EFA). L₁-norm EFA refines the factor estimation by minimizing the L1-norm of the residuals in the EFA model to reduce the impact of outliers using linear programming technique. A comprehensive analysis of L₁-norm EFA will be provided, focusing on its effectiveness in improving the stability and accuracy of factor analysis estimates in the presence of outliers. A simulation study will be applied to compare L₁-norm EFA with MCD and evaluate their performance and robustness in diverse data scenarios. Empirical results illustrate significant improvements in robustness compared to traditional factor analysis methods. Our method offers a practical solution for analysts dealing with noisy and outlier-prone datasets and more resilient framework for factor analysis.