Gram-Schmidt Transformation Minimization Algorithmnd Its Applications to Regression Analysis withulticollinearity
Date Issued
2008
Date
2008
Author(s)
Lin, Yu-Wei
Abstract
Regression analysis is the most used statistical method. However, we may encounter the multicollinearity problem in regression analysis. Multicollinearity is due to high correlation among independent variables, namely, small angles among data vectors of the independent variables.n the literature, there are two methods to orthogonalize vectors. One is the well-known Gram-Schmidt Process and the other is a method proposed by R.M. Johnson in 1966, referred to as the R.M. Johnson method. However, the Gram-Schmidt Process has no meaningful mechanism to determine the sequence order of vector orthogonalization; while the results transformed by the R.M. Johnson method can not be interpreted meaningfully, especially in a case with highly correlated data vectors.n this research, we attempt to develop an algorithm to determine the sequence order of the Gram-Schmidt Process with minimized transformation, called the Gram-Schmidt Transformation Minimization (GSTM) algorithm. It minimizes information subtraction during the vector projection processes. But before performing the GSTM algorithm, some procedures need to be done first. After those procedures, we perform the GSTM algorithm on data vectors, and with the orthogonalized data vectors, we perform regression analysis. Finally, we interpret the analysis results in regression analysis by the GSTM algorithm.e find that this proposed algorithm not only overcomes the multicollinearity problem in regression analysis and minimizes information subtraction during the vector projection processes but also makes the analysis results more interpretable.
Subjects
Regression Analysis
Multicollinearity
Gram-Schmidt Process
Information Transformation Minimization
Vector Projection
Type
thesis
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