Height–diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach

Height–diameter relationships based on stand characteristics (trees/ha, basal area, and dominant stand height) were investigated for balsam fir, balsam poplar, black spruce, jack pine, red pine, trembling aspen, white birch, and white spruce using data from permanent growth study plots in northern Ontario, Canada. Approximately half the data were used to estimate model parameters with the rest used for model evaluation. Multiple Chapman–Richards functions with parameters expressed in terms of various stand characteristics were fit to determine the best models for predicting height.Models providing the most accurate prediction of height included basal area, trees/ha, dominant stand height, and diameter at breast height (DBH). A mixed-effects modeling approach was applied in fitting the models for all tree species. Heights predicted by models including random-effects parameters (calibrated response) were compared with those developed without random-effects parameters (fixed-effects response). Including the random parameter consistently resulted in a better fit to the data (smaller AIC values) and an improved prediction accuracy.