Bias Correction in Logarithmic Regression and Comparison with Weighted Regression for Non-linear Models

Non-linear models with heteroscedasticity are commonly used in forestry modeling, and logarithmic regression and weighted regression are usually employed to estimate the parameters. Using the single-tree biomass data of large samples, the bias correction in logarithmic regression and comparison with weighted regression for non-linear models are studied in this paper. The immanent cause producing bias in logarithmic regression is analyzed, and a new correction factor is presented with which three commonly used bias correction factors are examined together, and the results show that the correction factors presented here and 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/f(x)2) presented by Zeng (1998) respectively, are compared with each other that show two weights works well and the general function is more applicable. It is suggested that the best way to fit non-linear models with heteroscedasticity would be using weighted regression, and when the total relative error of the estimates from the model fitted by the general weight function is more than a special limit such as ±3%, a better weight function based on residual errors of the model fitted by OLS should be used in weighted regression.