Comparison of nonlinear height–diameter functions for major Alberta tree species

Twenty nonlinear height–diameter functions were fitted and evaluated for major Alberta species based on a data set consisting of 13 489 felled trees for 16 different species. All functions were fitted using weighted nonlinear least squares regression (wi = 1/DBHi) because of the problem of unequal error variance. The examination and comparison of the weighted mean squared errors, the asymptotic t-statistics for the parameters, and the plots of studentized residuals against the predicted height show that many concave and sigmoidal functions can be used to describe the height–diameter relationships. The sigmoidal functions such as the Weibull-type function, the modified logistic function, the Chapman–Richards function, and the Schnute function generally gave the most satisfactory results.