关键词: 样本结构, 加权回归, 平均系统误差, 总体相对误差, 异方差

Abstract:

Sample structure and estimation method significantly influence the fitting accuracy of mathematical models.While the importance of estimation method is well-documented,the critical role of sample structure has received insufficient attention.This study designed eight sets of simulation datasets incorporating factors such as model complexity,data heteroscedasticity and sample homogeneity.Ordinary regression and weighted regression methods were applied to eight simulation datasets and their segmented samples to fit the biomass and tree height growth model.Six evaluation metrics were used to assess model fitting:coefficient of determination(R²),standard error of estimate(SEE),total relative error(TRE),average systematic error(ASE),mean prediction error(MPE),and mean percent standard error(MPSE).1)Under ideal modeling sample conditions,both heteroscedastic and homoscedastic models produced identical results using ordinary and weighted regression methods,with TRE and ASE values approaching zero.2)The sample structure emerged as the key determinant of modeling result,outweighing the choice of parameter estimation methods.3)The quality of sample structure depends not on the number of diameter or age(independent variable)classes,nor on the uniformity of sample size is distributed according to the independent variable classes,but on the even distribution of samples within each class.To enhance model accuracy,it is crucial to maximize coverage of the variation ranges of independent and dependent variables,divide independent variables into classes rationally,and scientifically allocate the samples sizes within each class.Emphasis should be placed on improving sample structure to ensure high-quality data for modeling.

Key words: sample structure, weighted regression, average systematic error, total relative error, heteroscedasticity