Additivity of nonlinear biomass equations

Abstract

Two procedures that guarantee the property of additivity among the components of tree biomass and total tree biomass utilizing nonlinear functions are developed. Procedure 1 is a simple combination approach, and procedure 2 is based on nonlinear joint-generalized regression (nonlinear seemingly unrelated regressions) with parameter restrictions. Statistical theory is given for construction of confidence and prediction intervals for the two procedures. Specific examples using slash pine (Pinus elliottii Engelm. var. elliottii) biomass data are presented to demonstrate and clarify the methods behind nonlinear estimation, additivity, error modeling, and the formation of confidence and prediction intervals. Theoretical considerations and empirical evidence indicate procedure 2 is generally superior to procedure 1. It is argued that modeling the error structure is preferable to using the logarithmic transformation to deal with the problem of heteroscedasticity. The techniques given are applicable to any quantity that can be disaggregated into logical components.