Treatment Of Multiplex Colinear Problems Based On Kernel Partial Least Square Regression

Multi-collinearity problems in models are often ignored in the current fields when using statistical regression analysis to build models to study problems.Multicollinearity is caused by the high correlation between variables.When the model has serious multicollinearity,the coefficient sign will be opposite to reality,and the parameter estimation will be difficult to pass the significance test to further make the model’s fitting effect poor or the model will fail So dealing with collinearity is particularly important for the model as a whole.This article compares the two common methods for dealing with multicollinearity problems-principal component regression and partial least squares regression.It is found that partial least squares regression analysis is superior to principal component regression analysis,but partial least squares regression model is essential It is a linear model.When the multi-collinearity problem exists in a nonlinear model,it cannot fit the complex relationship between variables well.In view of this shortcoming,this paper introduces a kernel function from the perspective of nonlinearity,and proposes a kernel partial least squares analysis method to deal with multicollinearity in nonlinear models.First,systematically elaborated the kernel method and the related theoretical principles of kernel partial least squares analysis.Kernel partial least squares extracts the main information components in the original variables to form a linearly independent kernel principal component to achieve the purpose of eliminating multicollinearity The algorithm steps and related program implementation of multi-collinearity in kernel partial least squares are given.Second,this paper divides the researched nonlinear models into three categories:nonlinear models with normal distribution of data,exponential models,general nonlinear models,and nonlinear models with dummy variables.For different types of non-linear models,given a range of parameters makes the introduction of the kernel function the best.The study found that except for ordinary non-linear models with dummy variables,Gaussian radial basis kernel functions cannot be used.The other three types of models are suitable for introducing Gaussian radial basis kernel functions.The nonlinear model with dummy variables is more suitable for the classification kernel function of multi-layer perceptron.Then,after determining the introduction of specific kernel functions for various types of nonlinear models,the partial least squares component extraction and the kernel partial least squares kernel principal component extraction are respectively carried out and the component regression model is established for multicollinearity diagnosis,multicollinearity problem Can be resolved.Finally,through an example,the specific application of kernel partial least squares in the treatment of multicollinearity in nonlinear models is analyzed.