Modeling and Prediction of Forest Growth Variables Based on Multilevel Nonlinear Mixed Models

In this article, we describe estimation and prediction methods for nonlinear modeling of forest growth variables that are subject to nested sources of variability. The multilevel nonlinear mixed- effects models that we consider are useful for a variety of forestry applications, but we concentrate on the problem of estimating, and making projections from, growth curves for tree height based on longitudinal data grouped by location. Wolfinger and Lin consider estimating equation approaches to fitting more general nonlinear mixed-effects models, and we adapt their zero-expansion estimating equations to the multilevel case. We develop methods of prediction based on these models that allow predictions of future height both for individual trees and for plot averages. We illustrate these methods by fitting and making predictions from a Chapman-Richards type growth model for tree height data from a loblolly pine spacing study in Putnam County, Georgia. The mean and variance of prediction errors based on our methods are examined by means of cross-validation. We provide a more complete and unified presentation of linearization-based estimation and prediction based on multilevel nonlinear mixed-effects models than has previously appeared in the forestry literature, and we argue that these models lead to substantial advantages in growth and yield prediction over traditional forestry methods. FOR. SCI. 47(3):311-321.