A tutorial on formalizing and testing specific psychological theory using nonlinear models

Nonlinear models represent exciting new opportunities for specifying and testing theory in ways that current linear models cannot. While linear models remain widespread and are relatively easy to estimate, the parameters of these models are often disconnected from specific psychological theories. Using nonlinear models, by contrast, allow us to test specific questions by linking model parameters to things we care about. Here, I will demonstrate promising uses of nonlinear models for formalizing and testing specific theory. First, I will show how we can use parameter moderation to model changes in the correlation between anxiety and depression within a nonlinear factor model. Then I showcase three examples in the regression and growth modeling space, demonstrating how nonlinear models can capture features of change, such as peaks and nonlinear transitions, that are not readily-available in linear models. Throughout, I use beginner-friendly language when discussing these topics and provide freely-available code resources for helping to specify and fit all models discussed. Readers will take away both a broad theoretical understanding of how nonlinear alternatives can better match statistical with theoretical models and offer specific hypothesis tests in psychology, as well as the practical skills for implementing the wide array of approaches within their own research domain.