Nonlinear Autoregressive Latent Trajectory Models

• In Event: 301 - Section on Methodology. Advances in Methods for Analyzing Longitudinal Data

Abstract

Autoregressive latent trajectory (ALT) models combine features of latent curve models (or trajectory models) and autoregressive models into a single modeling frame- work (Bollen and Curran, 2004). ALT models, however, have only been developed for linear latent trajectories, but many social processes follow nonlinear trajectories. This paper develops two classes of nonlinear autoregressive latent trajectory (NL-ALT) models. The first class allows for a quadratic growth trajectory, a popular extension among latent curve models. The second class allows for a nonparametric trajectory that allows for arbitrary growth processes. We first review the development of ALT models and their statistical properties. We then illustrate the model with empirical data for both classes of NL-ALT models. The empirical example involves modeling growth trajectories of weight from birth through late adolescence. We show that the model fit statistics and the predicted trajectories of weight growth prefer the NL-ALT model over either a linear ALT model or a nonlinear latent curve model. We conclude with a consideration of how to interpret the parameters of an NL-ALT model and the potential value of this class of models for applied social research.

Authors

• Shawn Bauldry, Purdue University

• Kenneth A. Bollen, University of North Carolina