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There is a growing interest among methodological and applied researchers in extending the use of regularization techniques (e.g., lasso regression, the elastic net) to structural equation models (SEMs). To date, most of the extensions have been based on combining the respective penalty function with the standard Maximum Likelihood fit function for SEMs. In the present article, we describe  two  ways in which the Two-Stage Least Squares (2SLS) estimator, an equation-by-equation estimator of SEMs, can be combined with these regularization techniques. Both approaches can be used to regularize the parameters in single equations (“local” regularization), and for both approaches, the parameters can be determined very quickly and efficiently using standard software. We evaluated the two methods in two simulation studies. We were able to show that both approaches provide suitable parameter estimates and can be used to select factor models and path coefficients even when the model is incorrectly specified.

Regularized 2SLS Estimation of Structural Equation Model Parameters