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 poses a difficult modeling scenario that entails large models with a comparably limited number of observations given the number of parameters. We here describe a particular strategy to overcoming this challenge, called regularization. Regularization, a method to penalize model complexity during estimation, has proven a viable option for estimating parameters in this small n, large p setting, but has so far mostly been used in linear regression models. Here 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 (Jacobucci, Grimm, & McArdle, 2016). Our approach is evaluated through the use of a simulation study, showing that regularized SEM outperforms traditional SEM estimation methods in situations with a large number of predictors and small sample size. We illustrate the power of this approach in two empirical examples: modeling the neural determinants of visual short term memory, as well as identifying demographic correlates of stress, anxiety and depression. We illustrate the performance of the method and discuss practical aspects of modeling empirical data, and provide a step-by-step online tutorial.
Keywords: LASSO; MIMIC; regularization; structural equation models; variable selection.