A LONGITUDINAL ANALYSIS OF HEIGHT DIAMETER CURVES/

The paper describes a simultaneous statistical analysis of height/diam eter 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 struc ture. Parameters of a logarithmic height/diameter curve at a given age in a given stand were decomposed into a trend (an age-dependent popul ation mean), a random stand effect, and a random time effect. The devi ation of an observed height from the stand and age specific height/dia meter curve was decomposed into a random tree effect and a random resi dual error which have nonhomogeneous variances. Trend functions for th e parameters of the height/diameter curve were estimated using least s quares estimates of parameters as dependent variables (generalized lea st squares would lead to inconsistent estimates). The trend equations describe most of the variation in the height curve parameters, Other s tand variables (in addition to age) can explain the variation further, but development over time cannot then be predicted. A less stable des cription of the height/diameter curves is obtained in terms of dominan t 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 s quares curves show erratic fluctuations.