Can ridge and elastic net structural equation modeling be used to stabilize parameter estimates when latent factors are correlated?

Scharf, F., Pförtner, J., & Nestler, S.

Abstract

Multicollinearity between predictors is a common concern in SEM applications. As in linear regression models, high correlations between predictors can lead to unstable parameter estimates (i.e., large standard errors) and reduced statistical power. Regularized estimation methods, which have recently become available for SEMs, may provide more stable estimates in the presence of multicollinearity at the cost of a certain amount of bias in the estimated parameters. In a simulation study, we compared the performance of nonregularized SEM with Ridge and Elastic net regularized SEMs in the presence of strong multicollinearity. The results provide evidence that Ridge and Elastic net regularized SEMs provide more stable estimates and greater statistical power than nonregularized SEM. However, the biases from regularized estimation can result in increased Type I error rates. This phenomenon was more pronounced in Ridge than in Elastic net regularized SEMs. We discuss when the benefits can outweigh this cost.