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Elimination of multicollinearity in the binary logistic regression model

Student: Oleg Yaksin

Supervisor: Elena R. Goryainova

Faculty: School of Applied Mathematics and Information Science

Educational Programme: Bachelor

Year of Graduation: 2014

<p>Binary Logistic regression model is the type of a regression model that estimates the probability of the belonging of an object to one of two classes. It is widely used in medicine, credit score, sociologic researches and other currently central areas.</p><p>The multicollinearity is the situation when some factors of regression model have high dependences, this fact can lead to a bad conditionality of a sampling matrix (a learning sample).Corrolary is that estimations of model parametric variables are labile, has big variances and signs that are in contrast to the theory.</p><p>In this paper Principal Component Analysis (PCA) is used to eliminate multicollinearity. The main idea of it is to find linear combinations of the factors called principal components that don&rsquo;t correlate among themselves at all. To evaluate principal components the covariance (corraletion) matrix of regressors is needed to be defined. The research of paper is based on method of forming a correlation matrix using Kramer and association coefficients. Using these coefficients is explained by that regressors can be nominal or have high linear or nonlinear dependences, that correlation coefficient identifies inaccurately.</p><p>With the help of modeled and real data it is shown that using method of the research in binary logistic regression model provides better predictive capability than models that don&rsquo;t use this method.</p>

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