互为自因变量模型的拟合可以采用对偶回归方法,但在应用时必须提供两个变量之间的误差结构关系,且统计之林(ForStat)中只在线性度量误差模型中涉及该方法的应用,给林业建模工作带来不便。利用东北地区100个红松林样地的优势高、平均高和平均胸径实测数据,分析了在拟合林分优势高与平均高模型、平均高与平均胸径模型时存在的两条回归线问题,进一步研究提出通过引入哑变量区分两条回归线,再采用非线性误差变量联立方程组或利用多元非线性回归估计方法求解各类互为自因变量模型参数的两种新方法。新方法不仅适用于林分优势高与平均高等常见的线性模型,也适用于林分平均高与平均胸径等非线性模型。

The dual regression method can be used to fit the mutual dependent variable models,however,the error structure relationship between the two variables must be provided in application,and this method is only applicable to the linear error-in-variable model in ForStat,which brings inconvenience to forestry modeling.Using the measured data of dominant height(H₀),mean height(H)and mean diameter at breast height(D)from 100 sample plots in Pinus koraiensis forests in northeastern China,this paper demonstrates two regression lines in fitting the H₀-H model and the H-D model.Two new methods are proposed by introducing dummy variables to distinguish two regression lines,followed by the use of nonlinear simultaneous equations with error-in-variables or multivariate nonlinear regression estimation method to estimate the parameters of mutual dependent variable models.These new methods are applicable not only to common linear models such as the H₀-H model,but also to nonlinear models such as the H-D model.