Differentiating between mixed-effects and latent-curve approaches to growth modeling.

In psychology, mixed-effects models and latent-curve models are both widely used to explore growth over time. Despite this widespread popularity, some confusion remains regarding the overlap of these different approaches. Recent articles have shown that the two modeling frameworks are mathematically equivalent in many cases, which is often interpreted to mean that one's choice of modeling framework is merely a matter of personal preference. However, some important differences in estimation and specification can lead to the models producing very different results when implemented in software. Thus, mathematical equivalence does not necessarily equate to practical equivalence in all cases. In this article, we discuss these two common approaches to growth modeling and highlight contexts in which the choice of the modeling framework (and, consequently, the software) can directly impact the model estimates, or in which certain analyses can be facilitated in one framework over the other. We show that, unless the data are pristine, with a large sample size, linear or polynomial growth, and no missing data, and unless the participants have the same number of measurements collected at the same set of time points, one framework is often more advantageous to adopt. We provide several empirical examples to illustrate these situations, as well as ample software code so that researchers can make informed decisions regarding which framework will be the most beneficial and most straightforward for their research interests.