Comparison of parametric and nonparametric methods for modeling height-diameter relationships

Abstract

This paper focuses on the problem of regionalization of the height-diameter model at the stand level. To this purpose, we selected two different modeling techniques. As a parametric method, we chose a linear mixed effects model (LME) with calibrated conditional prediction, whose calibration was carried out on randomly selected trees either close to mean diameter or within three diameter intervals throughout the diameter range. As a nonparametric method, the technique of classification and regression trees (CART) was chosen. These two methods were also compared with the local model created by ordinary least squares regression. The results show that LME with calibrated conditional prediction based on measurements of height at three diameter intervals provided results very close to the local model, especially when six to nine trees are measured. We recommend this technique for the regionalization of the global model. The CART method provided worse results than LME, with the exception of parameters of the residual distribution. Nevertheless, the latter approach is very user-friendly, as the regression tree creation and especially its interpretation are relatively simple, and could be recommended when larger deviations are allowed.

Keywords

• Calibration
• Classification and Regression Trees
• Hierarchical Structure
• Linear Mixed Effects Model
• Spatial Heterogeneity