1992/09/01 by Shongming Huang, Stephen J. Titus, Douglas P. Wiens · 5 citations
Engineering · Environmental Science · Mathematics · #Applied mathematics #Explained sum of squares #Forest ecology and management #Function (biology) #Logistic function #Mathematical analysis #Mathematics #Non-linear least squares #Nonlinear regression #Nonlinear system #Regression analysis #Sigmoid function #Soil Geostatistics and Mapping #Standard error #Statistics #Studentized range #Tree (set theory) #Weibull distribution #Wood Treatment and Properties
paper · doi:10.1139/x92-172
openalex publication_date 1992/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
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 (w i = 1/DBH i ) 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.