Relaxing the Proportionality Assumption in Latent Basis Models for Nonlinear Growth

Change over time is frequently nonlinear, which can present unique statistical challenges. Generally, different approaches for nonlinear growth engage in a tradeoff between interpretable parameters, expedient estimation, or how specific the model must be about the nature of the nonlinearity. Latent basis models are one method that can circumvent tradeoffs that other methods necessitate: it is quick to estimate, simple to interpret, and does not require specification of a particular trajectory. However, latent basis models require a restrictive proportionality assumption that is not required with other methods, which can limit its applicability with empirical data. This paper discusses this proportionality assumption and shows how it can be relaxed by reparameterizing the latent basis model as a multilevel structural equation model. We provide an example to show how relaxing proportionality can improve parameter estimates and person-specific growth curves. We also walkthrough Mplus code to facilitate fitting the model to empirical data.