Statistical Inference for Diameter-Height Curves using Varying Coefficient Model

Diameter-height curve is a function that defines the relationship between diameter at breast height and tree height. It is the mean trend on a scatter plot that shows the relationship between tree diameter at breast height and tree height. This curve shifts to the upper right corner as the tree ages in a uniformly aged plantation forest. Hence, it is commonly used to estimate the parameters of a model that describes the diameter-height curve by tree age. The transition in diameter-height curve with age can be interpreted as a change in the parameters of the model over time. However, the behavior of the parameters estimated independently from age-specific data may not accurately capture the features in the transition of the diameter-height curves, due to the variabilities of observations within each age of a forest stand. Against this background, in this paper, we introduce varying coefficients into the regression model for diameter-height curve to describe the transition of diameter-height curves as a function of time. The proposed method is then applied to a forest growth data of sugi (Cryptorneria japonica) stand in a village in Hoshino, Japan.