Study On Estimation Method And Application Of Regression Model In Forestry

The statistical analysis is one of the important tools that make the forestry conclusion become quantitative. How to apply the statistical analysis in forestry properly has gained more attention, while various statistical analysis methods are applied largely in forestry research. Some proberbles of estimating model in forestry are studied clearly in this paper, aiming at providing more scientific and efficient methods for statistical modeling in forestry. Multicollinearity, heteroscedasticity, measurement error model and consociation equation set model are further discussed in this paper.1. In chapter three, taking height-diameter multiple linear models of Pinus kesiya var. langbianensis as an example, the study on multicollinearity of 200 individual Pinus kesiya var. langbianensis data is made.When using the normal stepwise regression estimation, independent variable reduces from 9 to 4 though the multicollinearity in the model can not be eliminated. Because the multicollinearity in the model can not be removed through least squares regression and the stepwise regression base on least squares regression. The stepwise regression just screens out the variables that affect the tree-height unobviously. The multicollinearity in the model is studied in this paper,using the method of correlation matrix analysis, conditions index, tolerance, variance inflation factor and path analysis.The results show that there is multicollinearity in the model , in which two variance inflation factors are larger than 10.The height-diameter multiple linear models with the multicollinearity are studied in this paper by the ridge regression, principal component regression and partial least square regression.Results show that three kind methods all can eliminate the multicollinearity in the model, although their parameters estimation is different. The contrast analysis is carried on by variance inflation factor, in order to compare with the effects of three kind methods in eliminating multicollinearity. Results show ridge regression is the most effective method in eliminating multicollinearity. Contrasted with the principal component regression and partial least square regression, the ridge regression can justify the independent variables in the model, while the information can not be lost. The use of ridge regression is easy when using the method that variance inflation factor chooses k value. Basing on variance inflation factor, k value is 0.1370 by the ridge regression in height-diameter multiple linear models of Pinus kesiya var. langbianensis.The principal component regression and partial least square regression just process data with multicollinearity. Since the information lost, a deviation of regression coefficient may appear for excessively processing to the multicollinearity. According to different condition in the forestry modeling, selecting different method is the key thing. The study in this paper shows that the ridge regression is effective and logical in eliminating multicollinearity in the height-diameter multiple linear models of Pinus kesiya var.langbianensis.2. Taking the height-diameter multiple linear models of Pinus kesiya var.langbianensis and one-way volume model of larch as examples, the effect of heteroscedasticity is studied in chapter 4.Since the first is linear model, while the latter is nonlinear, there are representative to the study of heteroscedasticity in forestry model. Study shows that heteroscedasticity exists in the model by testing the model. Because of the different object and observating method of observation data in the forestry, the heteroscedasticity is unavoidable and differs in degree.Basing on former study, the research on heteroscedasticity in the height-diameter multiple linear models of Pinus kesiya var.langbianensis is made with twelve kinds of weighting function and four kinds of variable-weighting function. At the same time, the heteroscedasticiy to one-way volume model of larch is studied by eight kinds of weight function. The weighting function 1/x^2.334 is chosen to eliminate heteroscedasticity of height-diameter multiple linear models of Pinus kesiya var.langbianensis, while the weighting function 1/D²H is chosen to eliminate heteroscedasticity of one-way volume model of larch. The method of weighted regression estimate eliminating heteroscedasticity proves that various model has different optimal weight function form. When eliminating heteroscedasticity, various weight function forms should be tested in order to select the best one.The weight function is can not be constructed just by usual weight function form, although the heteroscedasticity in the model can also be eliminated, the result is unrefined and not best. For the sake of the precision, variable-weighting function should be used in selecting of the weight function. When heteroscedasticity shows linear structure, the r value of variable-weighting function is related to the intensity of the heteroscedasticity in the model, that is same model and different heteroscedasticity has various r. The stronger of heteroscedasticity in the model, the more deviation to zero of r value, oppositely, the nearer to zero of r value and the nearer to 1 of the weight function, which looks more like least squares regression. When the heteroscedasticity shows decrease in linear that is the linear slope of the variance is negative, r is positive. The slower of slope decreaed, the larger of r value, and vice versa.3. The effect of measurement error on the volume model V = aDbis studied in chapter five, and the parameter estimating is made by measurement errors, which draw following conclusions:With the increasing of deviation of dependent variable with measurement error,the estimating parameters fluctuates and becomes unsteady in trend,when measure error exists in dependent variable but constrarily in independent variable. The measurement error of dependent variable affe cts to the model parameter estimating thus, it is not the optimal estimating method that using genearal nonlinear regression method when estimating the parameters in volume model. Oppositely, when the independent variable has measurement error and the dependent variable has none, the results show the same, and the measure error of independent variable also affects model parameter estimating. In usual nonlinear regression method, hypothesis that independent variable has no error or its error is unimportant and the error has no effect to the model are unscientific.Similar to the other observation data in forestry, the independent variable and the dependent variable in the volume model are collected by different measurement tool and observating method, the measurement error is inevitable in the model. Parameter estimating is a complicated issue when dependent variable and independent variable both have measurement error. Since independent variable is deemed to no error in usual nonlinear regression,thus, the parameter estimating of volume model can't be made in this way,while the measurement error model method is suitable for the condition that measurement error estist in dependent variable and independent variable .The variance of volume V is 0.5678 using usual nonlinear regression methods while it is 0.4450 using measurement error model methods,which results that the variance of model becomes smaller and more accords with the variance least in statistical principle. When the measurement error of dependent variable becomes bigger, the estimation parameter using the normal method is not unbiased estimation and validates the practice. But measurement error method can get an unbiased estimation, only if the error matrix is estimated more exactly. It provides a more valid method of fitting actual circumstance for the parameter estimation of volume model with measurement error.4.Taking larch as an example, the application of consociation equation set model in constructing duality standing tree volume model and the advantage of two steps estimations method in estimating consociation equation set model are discussed in chapter six, which obtains better effect.It is the first time that consociation equation set model method is applied in creating duality standing tree volume model in this paper, which matches the modeling principle of duality standing tree volume model. In duality standing tree volume model, the average tree-height is estimated baed on diameter-height curve equation, which can be realized directly in consociation equation set model instead of traditional method step by step. Simultaneity this method can make diameter-height curve equation and the volume model has compatibility to same tree kind. In the estimation of consociation equation set model, two steps estimation method which is seldom used in the forestry is used in this paper. The relative system error RS equates -0.1737, the average relative error E equates -2.6279 when using two steps estimation, which are more closed to 0 than that RS equates -0.4615 and E equates -4.1514 when using usual nonlinear regression method. As a result, this method can not only make the parameter estimation is unbiased, but also can reduce system error in the parameter estimation, two steps estimation method is better than usual nonlinear estimation in the estimation of consociation equation set model.The consociation equation set model and two steps estimation methods in this paper have certain superiority in parameter estimating of duality standing tree volume model. This method is simple, easy working and superior to traditional method.