L0 and Lp loss functions in model-robust estimation of structural equation models

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.