Measurement error causes bias in site index equations

Abstract

Modeling height in the context of site index involves two processes: (i) estimating height at base age (site index), given height at some other age, and (ii) estimating height at some desired age given height at base age. When these two processes are modeled by individual functions for each process, height is assumed to be measured without error when on the right-hand side of the equation, but possessing error when on the left-hand side of the equation. This assumption causes a bias in the parameters of the site index curves. The bias in the estimated parameters is evident in the magnitude of the curves and in the shape of the curves, the typical change of shape of the curves from low site index to high site index is underestimated. An ad hoc method is presented that solves the problem. The ad hoc method is conceptually related to methods used in linear regression and to maximum likelihood estimation in a measurement errors problem context. A general measurement errors model is presented as an alternative. The measurement errors model requires an independent estimate of measurement error.