Generalized Height-Diameter Models with Mixed Effects Parameters Diffusion Processes

Abstract

Statistical models using stochastic differential equations (SDEs) to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. The generalized height-diameter equations were developed in order to predict the total height of individual trees in uneven-aged stands. In this study, models based on a Vasicek non-homogeneous diffusion process are formulated. The drift function depends on deterministic function that describes the dynamic of certain exogenous stand variables (crown height, CH, crown width, CW, mean diameter at breast height, D0, mean height, H0, age, A, soil fertility index, SFI, stocking level, S). The mixed-effects parameters SDEs models included a random parameter that affected the models asymptote. The parameter estimators are evaluated by maximum likelihood procedure. The objective of the research was to develop a generalized height–diameter SDEs models and to illustrate issues using dataset of Scots pine trees (Pinus sylvestris L.) in Lithuania with diameter at breast height outside the bark larger than 0 cm. The parameters of all used models were estimated using an estimation data set and were evaluated using a validation data set. The new developed generalized mixed-effects parameters SDEs height-diameter models are an improvement over exogenous stand variables in that it can be calibrated to a new stand with observed height-diameter pairs, thus improving height prediction.