On the Estimation of Nonlinear Mixed-Effects Models and Latent Curve Models for Longitudinal Data

Abstract

Nonlinear models are effective tools for the analysis of longitudinal data. These models provide a flexible means for describing data that follow complex forms of change. Exponential and logistic functions that include a parameter to represent an asymptote, for instance, are useful for describing responses that tend to level off with time. There are forms of nonlinear latent curve models and nonlinear mixed-effects model that are equivalent, and so given the same set of data, growth function, distributional assumptions, and method of estimation, the 2 models yield equivalent results. There are also forms that are strikingly different and can yield different interpretations for a given set of data. This article discusses cases in which nonlinear mixed-effects models and nonlinear latent curve models are equivalent and those in which they are different and clarifies the estimation needs of the different models. Examples based on empirical data help to illustrate these points.