Comparison of seemingly unrelated regressions with error-in-variable models for developing a system of nonlinear additive biomass equations

Abstract

Nonlinear error-in-variable models can advance the development of the systems of additive biomass equations and lead to much higher prediction accuracy of tree biomass than nonlinear seemingly unrelated regression. In this study, the approach of nonlinear error-in-variable models (NEIVM) was compared with nonlinear seemingly unrelated regressions (NSUR) for developing a system of nonlinear additive biomass equations using the data collected in Southern China for Pinus massoniana Lamb. Various tree variables were assessed to explore their contributions to improvement of biomass prediction using the systems of equations. It was found that diameter at breast height (D), total tree height (H) and crown width (CW) significantly contributed to the increase of prediction accuracy. The combinations of D, H, and CW led to three sets of independent variables: (1) D alone; (2) both D and H; and (3) D, H and CW together, which were used for the development of one-predictor, two-predictor and three-predictor systems of biomass equations, respectively. The results showed that both NEIVM and NSUR had high prediction accuracy of biomass for all the systems of biomass equations. For the one-predictor systems of biomass equations, both NEIVM and NSUR led to very similar predictions. However, for the two-predictor and three-predictor systems of biomass equations, the prediction accuracy of NEIVM was much higher than that of NSUR. When the two-predictor system of equations was used, in particular, NEIVM with one-step procedure, that is, by directly partitioning total tree biomass into four basic components, showed a higher accuracy of biomass prediction than NSUR for all the one-predictor, two-predictor and three-predictor systems of equations. This study implies that the NEIVM approach could provide a greater potential to develop a system of biomass equations that are dependent on the predictors with significant measurement errors.