Fitting Methods of Mutual Dependent Variable Models in Forestry

doi:10.13466/j.cnki.lczyyj.2024.04.009

Abstract

Abstract:

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.

Key words: mutual dependent variable, two regression lines, dual regression, dummy variable, simultaneous equations, multivariate regression

CLC Number:

S757.1

ZENG Weisheng. Fitting Methods of Mutual Dependent Variable Models in Forestry[J]. Forest and Grassland Resources Research, 2024, (4): 78-83.

Figures/Tables 5

Tab.1

Tab.2

Tab.3

Tab.4

Fig.1

References 13

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变量	最小值	最大值	平均值	标准差	变动系数/%
优势高(H₀)	8.61	29.67	20.96	4.65	22.20
平均高(H)	7.42	24.08	16.86	3.59	21.30
平均胸径(D)	10.98	35.52	22.75	5.43	23.89

模型	a₀	a₁	b₀	b₁
(1)	0.822	1.195	(-0.688)	(0.837)
(2)	(-2.727)	(1.405)	1.940	0.711 6
(4)	1.573	0.761	(0.552)	(1.314)
(5)	(0.728)	(1.006)	1.371	0.994 3

方法	联立模型	a₀	a₁	b₀	b₁
非线性误差变量联立方程组	(7)	-0.037	1.247	0.030	0.801
非线性误差变量联立方程组	(8)	1.140	0.864	0.859	1.158
多元非线性回归估计	(9)	-0.037	1.247	0.030	0.801
多元非线性回归估计	(10)	1.123	0.869	0.875	1.151

方法	模型	Q_合	R²	E_SE/m	E_MPS/%
独立估计1	(1)	546	0.850	1.81	7.68
	(2)	546	0.824	1.51	7.99
	(4)	1 149	0.778	1.70	8.83
	(5)	1 149	0.704	2.97	11.95
独立估计2	(1)	569	0.824	1.96	8.14
	(2)	569	0.850	1.40	7.00
	(4)	1 057	0.704	1.96	10.00
	(5)	1 057	0.768	2.63	9.65
联立估计1	(1)	533	0.848	1.82	7.62
	(2)	533	0.837	1.46	7.56
	(4)	1 026	0.763	1.76	9.19
	(5)	1 026	0.753	2.72	10.60
联立估计2	(1)	533	0.848	1.82	7.62
	(2)	533	0.837	1.46	7.56
	(4)	1 028	0.764	1.75	9.16
	(5)	1 028	0.751	2.72	10.61

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