Exploring the error structure of taper equations

Abstract

Much work has been done fitting taper equations to specific tree bole shapes, but few researchers have investigated what effect the correlated error structure has on the fit of a taper equation. The Max and Burkhart (1976) taper equation was used in conjunction with a number of equations which modeled the covariance structures. The equations proposed were continuously differentiable, which simplifies the fitting process, and selected to minimize the number of parameters. A maximum likelihood method was proposed to fit these equations and test the statistical significance of the correlated errors. Accounting for the correlated errors structure in the equation fitting process significantly improved fit. Tests showed a small, but significant, bias of 1.05% (± 0.143%) when the correlated errors were ignored.