<i>L</i>₀ and <i>L</i>_p Loss Functions in Model-Robust Estimation of Structural Equation Models

Abstract

The Lp loss function has been used for model-robust estimation of structural equation models based on robustly fitting moments. This article addresses the choice of the tuning parameter ε that appears in the differentiable approximations of the nondifferentiable Lp loss functions. Moreover, model-robust estimation based on the Lp loss function is compared with a recently proposed differentiable approximation of the L0 loss function and a direct minimization of a smoothed version of the Bayesian information criterion in regularized estimation. It turned out in a simulation study that the L0 loss function slightly outperformed the Lp loss function in terms of bias and root mean square error. Furthermore, standard errors of the model-robust SEM estimators were analytically derived and exhibited satisfactory coverage rates.

Keywords

• structural equation modeling
• model-robust estimation
• differentiable approximation
• robust loss function
• regularized estimation
• BIC