Nonlinear mixed-effects modeling of cumulative bole volume with spatially correlated within-tree data

• Published in: Journal of agricultural, biological, and environmental statistics Vol. 1; no. 1; pp. 107 - 119
• Main Authors: Gregoire, T.G, Schabenberger, O
• Format: Journal Article
• Language: English
• Published: American Statistical Association and the International Biometric Society 01-03-1996
• Subjects: Biometrics; Data models; Estimators; forest inventory; forest mensuration; Forestry; mathematics and statistics; Modeling; Multilevel models; Musical intervals; Parametric models; Tree trunks; Trees
• ISSN: 1085-7117; 1537-2693
• DOI: 10.2307/1400563

Equations to predict the volume of an individual tree bole between stump height and the height at which its diameter has tapered to a specified minimum are common in forestry. When fitting such a regression equation, a sample of trees which span the range of sizes needed for eventual application of the equation is selected. Bole diameter is measured at ascending heights on the bole. Each tree, therefore, contributes multiple measurements to the data fitted to the equation. In contrast to past practice, we model these data in a manner which accounts for the likely spatial correlation among measurements within a tree. The resulting mixed-effects nonlinear model is fitted by restricted maximum likelihood (REML) and also by generalized estimating equations (GEE). Results from the two approaches are nearly identical, which suggests that the computationally less demanding GEE may be acceptable as a routine alternative to a fully parameterized approach.