An approach to multicollinearity problem with independent components analysis

In the first part of the thesis, although it is a multivariate statistical method, Independent Components Analysis which is mostly used in the engineering field, which is not known much in statistics, has been discussed in detail and has been contributed to the limited Turkish literature. Secondly, a new solution was proposed by Independent Components Analysis to the multicollinearity problem, which is one of the most common problems in multiple linear regression analysis, which caused the assumption distortions and caused negative effects on the regression model. Thus, it has been shown that the analysis can be used as a tool for different purposes in addition to its current uses. In this context, a new method has been developed based on Independent Components Analysis, which is similar to the operation of biased regression methods such as Principal Components Regression and Partial Least Squares Regression used to solve multicollinearity problem. The novel contribution of this method to the literature is that the use of mutual information, a concept in the field of entropy, is proposed in the selection of independent components to be included in multiple linear regression analysis. The performance of the developed method was evaluated separately on artificial and real datasets. As a result, it was determined that the proposed method based on Independent Components Analysis can be used to solve the multicollinearity problem, estimation and prediction can be made with lower error amount than other biased regression methods for the explained (dependent) variable in the regression analysis, and regression coefficients can be estimated with lower standard errors. Keywords: Independent Components Analysis, Principal Component Analysis, Regression Analysis, Multicollinearity Problem, Principal Component Regression, Independent Component Regression, Shannon Entropy, Mutual Information.