Development of Nonlinear Parsimonious Forest Models Using Efficient Expansion of the Taylor Series: Applications to Site Productivity and Taper

Abstract

The parameters of nonlinear forest models are commonly estimated with heuristic techniques, which can supply erroneous values. The use of heuristic algorithms is partially rooted in the avoidance of transformation of the dependent variable, which introduces bias when back-transformed to original units. Efforts were placed in computing the unbiased estimates for some of the power, trigonometric, and hyperbolic functions since only few transformations of the predicted variable have the corrections for bias estimated. The approach that supplies unbiased results when the dependent variable is transformed without heuristic algorithms, but based on a Taylor series expansion requires implementation details. Therefore, the objective of our study is to investigate the efficient expansion of the Taylor series that should be included in applications, such that numerical bias is not present. We found that five functions require more than five terms, whereas the arcsine, arccosine, and arctangent did not. Furthermore, the Taylor series expansion depends on the variance. We illustrated the results on two forest modeling problems, one at the stand level, namely site productivity, and one at individual tree level, namely taper. The models that are presented in the paper are unbiased, more parsimonious, and they have a RMSE comparable with existing less parsimonious models.