Height diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose the method- ology of stochastic differential equati...Height diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose the method- ology of stochastic differential equations that is derived from the standard deterministic ordinary differential equation by adding the process variability to the growth dynamic. Age-diameter varying height model was deduced using a two-dimensional stochastic Gompertz shape process. Another focus of the article is the investigation of normal cop- ula procedure, when the tree diameter and height are governed by univariate stochastic Gompertz shape processes. The advantage of the stochastic differential equation method- ology is that it analyzes a residual variability, corresponding to measurements error, and an individual variability to represent heterogeneity between subjects more complex than commonly used fixed effect models. An analysis of 900 Scots pine （Pinus sylvestris） trees provided the data for this study.展开更多
文摘Height diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose the method- ology of stochastic differential equations that is derived from the standard deterministic ordinary differential equation by adding the process variability to the growth dynamic. Age-diameter varying height model was deduced using a two-dimensional stochastic Gompertz shape process. Another focus of the article is the investigation of normal cop- ula procedure, when the tree diameter and height are governed by univariate stochastic Gompertz shape processes. The advantage of the stochastic differential equation method- ology is that it analyzes a residual variability, corresponding to measurements error, and an individual variability to represent heterogeneity between subjects more complex than commonly used fixed effect models. An analysis of 900 Scots pine （Pinus sylvestris） trees provided the data for this study.
