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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 …