A Practical Guide to Variable Selection in Structural Equation Modeling by Using Regularized Multiple-Indicators, Multiple-Causes Models

Methodological innovations have allowed researchers to consider increasingly sophisticated statistical models that are better in line with the complexities of real-world behavioral data. However, despite these powerful new analytic approaches, sample sizes may not always be sufficiently large to deal with the increase in model complexity. This difficult modeling scenario entails large models with a limited number of observations given the number of parameters. Here, we describe a particular strategy to overcome this challenge: regularization, a method of penalizing model complexity during estimation. Regularization has proven to be a viable option for estimating parameters in this small-sample, many-predictors setting, but so far it has been used mostly in linear regression models. We show how to integrate regularization within structural equation models, a popular analytic approach in psychology. We first describe the rationale behind regularization in regression contexts and how it can be extended to regularized structural equation modeling. We then evaluate our approach using a simulation study, showing that regularized structural equation modeling outperforms traditional structural equation modeling in situations with a large number of predictors and a small sample size. Next, we illustrate the power of this approach in two empirical examples: modeling the neural determinants of visual short-term memory and identifying demographic correlates of stress, anxiety, and depression.