A longitudinal analysis of height/diameter curves

Abstract

The paper describes a simultaneous statistical analysis of height/diameter curves in data consisting of several temporal and permanent plots. Two jack pine data sets, one from planted stands and the other from naturally regenerated stands, were analyzed using the same model structure. Parameters of a logarithmic height/diameter curve at a given age in a given stand were decomposed into a trend (an age-dependent population mean), a random stand effect, and a random time effect. The deviation of an observed height from the stand and age specific height/diameter curve was decomposed into a random tree effect and a random residual error which have nonhomogeneous variances. Trend functions for the parameters of the height/diameter curve were estimated using least squares estimates of parameters as dependent variables (generalized least squares would lead to inconsistent estimates). The trend equations describe most of the variation in the height curve parameters. Other stand variables (in addition to age) can explain the variation further, but development over time cannot then be predicted. A less stable description of the height/diameter curves is obtained in terms of dominant height. In applications, height/diameter curves can be calibrated by predicting the random stand and time effects using any combination of height measurements. A simultaneously estimated set of curves will be logical also when there are so few measurements that ordinary least squares curves show erratic fluctuations.