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Logistic回归多重共线性的诊断与改进及其在医学中的应用

Logistic Regression Multiple Linear Diagnosis and Improvement and Its Application in Medicine

【作者】 周菲

【导师】 焦桂梅;

【作者基本信息】 兰州大学 , 应用数学, 2011, 硕士

【摘要】 本论文研究了Logistic回归模型多重共线性的诊断与改进方法,解决了医学研究中由自变量的多重共线性造成的模型系数不稳定、结论难以解释等问题;便于医学研究者正确合理的建立Logistic回归模型,处理混杂因素,预测疾病和判别分类。对于Logistic回归模型多重共线性的诊断主要采取了医学研究中适用的变量间的二元相关系数r、方差膨胀因子VIF、容许值TOL、特征根分析等方法。对Logistic回归模型多重共线性的改进方法主要介绍了主成分回归,即在信息损失不大和实际应用需要的条件下,通过提取主成分,将相关关系较高的变量信息综合成相关性较低的若干个主成分,然后以主成分代替原变量参与回归,使彼此相关的变量间独立;简单介绍了偏最小二乘法对Logistic回归模型多重共线性的改进处理。通过实例分析,与多元线性回归一样,Logistic回归模型也对多重共线性敏感。在医学研究中,尤其是在流行病的发病因素分析中,应用主成分回归以及偏最小二乘回归进行多重共线性的改进处理,可以削减自变量观察矩阵之间的多重共线性,建立较为理想的关系模型,提高结果的可靠性。全部计算过程采用SPSS17.0统计软件。

【Abstract】 This thesis studies the diagnosis and enhancing methods of the multi-collinearity of logistic regression model, to solve the problems caused by the multi-collinearity of variables in medical research, such as the instability of model coefficients and difficulty in conclusion explanations, and finally to enable medical researchers to establish correct and reasonable logistic regression model, deal with mixed factors, conduct disease predictions and identify and categorize them,In order to diagnose the multi-collinearity of logistic regression model, the author mainly adopts the following methods applicable in medical research:binary correlation coefficient r, variance inflation factor VIF, tolerance TOL, eigenvalue analysis. In connection with the enhancing methods, the author chiefly introduces principal component regression, namely, on condition that the loss of information is not significant and practical application is needed, to integrate the information of variables of originally higher interrelatedness into a certain number of main ingredients of lower interrelatedness, then substitute main ingredients for original variables and involve them in regression for the separation of interrelated variables. In addition, the author makes a brief introduction of the improvements conducted by partial least squares regression on logistic regression model.Through case analyses, Like multiple linear regression, logistic regression model is of same sensitivity to multi-collinearity. It can be concluded: in medical research, especially in the analyses of pathological factors of epidemics, the application of principal component regression and partial least squares regression to the improvements of multi-collinearity can reduce the multi-collinearity between matrices of variables, build up relatively ideal relation models and improve the reliability of results. SPSS 17.0 statistical software is employed in all calculations.

  • 【网络出版投稿人】 兰州大学
  • 【网络出版年期】2012年 06期
  • 【分类号】R195
  • 【被引频次】16
  • 【下载频次】1306
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