Estimation of Time-Unstructured Nonlinear Mixed-Effects Mixture Models

Abstract

Change over time often takes on a nonlinear form. Furthermore, change patterns can be characterized by heterogeneity due to unobserved subpopulations. Nonlinear mixed-effects mixture models provide one way of addressing both of these issues. This study attempts to extend these models to accommodate time-unstructured data. We develop methods to fit these models in both the structural equation modeling framework as well as the Bayesian framework and evaluate their performance. Simulations show that the success of these methods is driven by the separation between latent classes. When classes are well separated, a sample of 200 is sufficient. Otherwise, a sample of 1,000 or more is required before parameters can be accurately recovered. Ignoring individually varying measurement occasions can also lead to substantial bias, particularly in the random-effects parameters. Finally, we demonstrate the application of these techniques to a data set involving the development of reading ability in children.

Keywords:

• growth mixture model
• longitudinal
• mixed-effects model
• nonlinear

Additional information

Funding

Sarfaraz Serang was supported in part by Grant AG 007137-25 from the National Institutue on Aging. Kevin J. Grimm was supported by National Science Foundation Grant REAL-1252463 awarded to the University of Virginia, David Grissmer (Principal Investigator), and Christopher Hulleman (Co-Principal Investigator).