Developing Forest Models from Longitudinal Data : A Case Study Assessing the Need to Account for Correlated and/or Heterogeneous Error Structures under a Nonlinear Mixed Model Framework(<Special Issue>Multipurpose Forest Management)

Abstract

In this study we demonstrated the procedures for model estimation and prediction based on the nonlinear mixed model (NLMM) technique. Since the unequally spaced and unbalanced longitudinal data used to fit forest models are often correlated and unequally varied, generalized error structures were examined and compared to the independent and identically distributed (iid) structure. In addition, since the vast majority of forest models are developed to be used as predictive tools on new data once the model coefficients have been estimated, predictions from the fitted model with and without accounting for the generalized error structures were evaluated on both model fitting and independent model validation data sets. Results showed that, under the NLMM framework, the iid structure is a superior choice for addressing correlated and heteroscedastic errors, provided that the model is appropriate for the data. This outcome has important practical implications, as a simpler error structure can achieve better predictions than more complex structures. The theoretical and practical consequences of ignoring or accounting for the error structure in NLMM estimation and prediction are discussed.