Bias Correction in Logarithmic Regression and Comparison with Weighted Regression for Nonlinear Models

Abstract

Non-linear models with heteroscedasticity are commonly used in ecological and forestry modeling, and logarithmic regression and weighted regression are usually employed to estimate the parameters. Using the single-tree biomass data of three large samples, the bias correction in logarithmic regression for non-linear models was studied and comparison between logarithmic regression and weighted regression was discussed in this paper. Firstly, the imminent cause producing bias in logarithmic regression was analyzed, and a new correction factor was presented with which three commonly used bias correction factors were examined together, and the results showed that the correction factors presented here and derived by Baskerville (1972) should be recommended, which could insure the corrected model to be asymptotically consistent with that fitted by weighted regression. Secondly, the fitting results of weighted regression for non-linear models, using the weight function based on residual errors of the model estimated by ordinary least squares (OLS) and the general weight function (w=1/ƒ(x)2) presented by Zeng (1998) respectively, were compared with each other that showed two weight functions worked well and the general function was more applicable. It was suggested that the best way to fit non-linear models with heteroscedasticity would be using weighted regression, and if the total relative error of the estimates from the model fitted by the general weight function was more than a special allowance such as ±3%, a better weight function based on residual errors of the model fitted by OLS should be used in weighted regression.