Impact of bias in predicted height on tree volume estimation: A case-study of intrinsic nonlinearity

Abstract

Bias originating from intrinsic nonlinearity in nonlinear models is caused by excess curvature in the solution locus of parameter estimates derived from least squares procedures. Bias due to intrinsic nonlinearity varies according to sample size as well as model specification. This paper analyses consequences of fractionising data into smaller sub-samples. Based on measurements of stem diameter and total tree height from the first Danish national forest inventory, it is demonstrated how data splitting at random may cause the intrinsic nonlinear curvature to exceed the critical F-value. Application of a Taylor-series expansion shows that, for all practical purposes, the bias in predictions of individual tree volume (based on stem diameter and tree height) is negligible. To minimize residual variance, intrinsic curvature and, in turn, prediction bias, it is recommended that data be stratified according to site conditions, stand characteristics or other relevant criteria. Finally, the preferred model should exhibit close-to-linear behaviour. (c) 2009 Elsevier B.V. All rights reserved.

Keywords

Bias in regression predictor; Box's bias; Forest inventory data; Intrinsic curvature; Nonlinear regression; Parameter effects curvature; Sample size; Wood volume estimation

Published in

Ecological Modelling
2009, volume: 220, number: 20, pages: 2656-2664

SLU Authors

• Skovsgaard, Jens Peter

  • University of Copenhagen

UKÄ Subject classification

Forest Science

Publication identifier

• DOI: https://doi.org/10.1016/j.ecolmodel.2009.06.048

Permanent link to this page (URI)

https://res.slu.se/id/publ/90133