Statistical modeling and design in forestry : The case of single tree models

Forest quantification methods have evolved from a simple graphical approach to complex regression models with stochastic structural components. Currently, mixed effects models methodology is receiving attention in the forestry literature. However, the review work (Paper I) indicates a tendency to overlook appropriate covariance structures in the NLME modeling process. A nonlinear mixed effects modeling process is demonstrated in Paper II using Cupressus lustanica tree merchantable volume data and compared several models with and without covariance structures. For simplicity and clarity of the nonlinear mixed effects modeling, four phases of modeling were introduced. The nonlinear mixed effects model for C. lustanica tree merchantable volume with the covariance structures for both the random effects and within group errors has shown a significant improvement over the model with simplified covariance matrix. However, this statistical significance has little to explain in the prediction performance of the model. In Paper III, using several performance indicator statistics, tree taper models were compared in an effort to propose the best model for the forest management and planning purpose of the C. lustanica plantations. Kozak's (1988) tree taper model was found to be the best for estimating C. lustanica taper profile. Based on the Kozak (1988) tree taper model, a Ds optimal experimental design study is carried out in Paper IV. In this study, a Ds-optimal (sub) replication free design is suggested for the Kozak (1988) tree taper model