Generalized fixed-effects and mixed-effects parameters height–diameter models with 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. In this study, the SDE mixed-effects parameter models based on a Vasicek non-homogeneous diffusion process are formulated. The breast height diameter-dependent drift function additionally depends on deterministic function that describes the dynamic of certain exogenous stand variables (crown height, ch, crown width, cw, mean breast height diameter, d0, mean height, h0, age, A, soil fertility index, SFI, stocking level, S) versus breast height diameter. The mixed-effects parameters SDE 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 mixed-effects parameters SDE height–diameter models and to illustrate issues using dataset of Scots pine trees (Pinus sylvestris L.) in Lithuania with the breast height diameter outside the bark larger than 0 cm. The parameters of all used models were estimated using an estimation dataset and were evaluated using a validation dataset. The new developed 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.