Comparison of different methods for fitting nonlinear mixed forest models and for making predictions

Abstract

Nonlinear mixed models have become popular in forestry applications, and various methods have been proposed for fitting such models. However, it is difficult or even confusing to choose which method to use, and there is not much relevant information available, especially in the forestry context. The main objective of this study was to compare three commonly used methods for fitting nonlinear mixed models: the first-order, the first-order conditional expectation, and the adaptive Gaussian quadrature methods. Both the maximum likelihood and restricted maximum likelihood parameter estimation techniques were evaluated. Three types of data common in forestry were used for model fitting and model application. It was found that the first-order conditional expectation method provided more accurate and precise predictions for two models developed from data with more observations per subject. For one model developed on data with fewer observations per subject, the first-order method provided better model predictions. All three models fitted by the first-order method produced some biologically unrealistic predictions, and the problem was more obvious on the data with fewer observations per subject. For all three models fitted by the first-order and first-order conditional expectation methods, the maximum likelihood and restricted maximum likelihood fits and the resulting model predictions were very close.