Comparison of Regression Methods for Fitting Allometric Equations to Biomass of Mizunara Oak(Quercus crispula)

Abstract

This study examined the use of linear and non-linear regression techniques for estimating parameters of allometric equations for the biomass of mizunara oak (Quercus crispula Blume) trees growing in deciduous secondary forests that are dominated by the species. Four plots were sampled in secondary forests and 31 mizunara oak trees were sampled outside the experimental plots to measure biomass. Three typical allometric equations used for biomass estimation were fitted to the mass of each component and the sum of some components using three least-squares regression methods: non-linear regression without weighting observations, generalized non-linear regression assuming that the variance of each observation was expressed as a power function of the corresponding mean value, and linear regression after fitting a logarithmically transformed function to logarithms of the data. Errors in the predictions were compared among the three regression models. The fitted allometric equations were applied to tree census data from the experimental plots to examine variation in stand biomass estimates among the three regression methods. In terms of errors, generalized non-linear regression was slightly preferable to logarithmic linear regression and unweighted non-linear regression. Branch mass and foliage mass had different values of variance parameter (half of the exponent of the power function), even though both showed large variation around their regression lines. When the variance parameter was greater than 1.0, as occurred with branch mass, logarithmic linear regression was slightly better than generalized non-linear regression. When applying fitted allometric equations to other data, the three regression methods may produce only slightly different estimates of stem mass; however, estimates for branch mass and foliage mass may differ largely according to the regression method used.