Heteroskedasticity

An apparent challenge in the modelling of biomass is heteroskedasticity. This effect of growing variance with growing dimension of trees is characteristic of tree data. The problem is that heteroskedasticity (in-homogeneity of variances) violates a basic assumption of ordinary least squares regression (van Laar and Akga 2007).

To solve this problem, transformations are often applied to the data, which have the positive side effect that the well-established framework of linear regression can be used instead of nonlinear statistics. However, this transformation process comes with the flaw that the estimation is biased after back-transformation and has to be corrected. Different methods have been suggested for bias correction (Finney 1941; Baskerville 1972; Yandle and Wiant 1981; van Laar and Akqa 2007). Alternative estimation methods to ordinary least squares regression have been proposed to deal with the problem of heteroskedasticity. Linear weighted least squares and iterative non-linear least squares regression (for nonlinear relationships) methods showed good results (Verwust 1991; Parresol 2001). With growing computing capacity weighted nonlinear least squares estimation might be the most elegant choice to avoid transformation bias and heteroskedasticity (Schabenberger and Pierce 2002).