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A Comparative Study On Some Methods For Handling Multicollinearity Problems

A Comparative Study On Some Methods For Handling Multicollinearity Problems
In regression, the objective is to explain the variation in one or more response variables, by associating this variation with proportional variation in one or more explanatory variables. A frequent obstacle is that several of the explanatory vari- ables will vary in rather similar ways. As a result, their collective power of explanation is considerably less than the sum of their individual powers. This phenomenon called multicollinearity, is a common problem in regression analysis. Handling multicollinear- ity problem in regression analysis is important because least squares estimations as- sume that predictor variables are not correlated with each other. The performances of ridge regression (RR), principal component regression (PCR) and partial least squares regression (PLSR) in handling multicollinearity problem in simulated data sets are compared to help and give future researchers a comprehensive view about the best procedure to handle multicollinearity problems. PCR is a combination of principal component analysis (PCA) and ordinary least squares regression (OLS) while PLSR is an approach similar to PCR because a component that can be used to reduce the number of variables need to be constructed. RR on the other hand is the modified least square method that allows a biased but more precise estimator. The algorithm is described and for the purpose of comparing the three methods, simulated data sets where the number of cases were less than the number of observations used. The goal was to develop a linear equation that relates all the predictor variables to a response variable. For comparison purposes, mean square errors (MSE) were calculated. A Monte Carlo simulation study was used to evaluate the eectiveness of these three procedures. The analysis including all simulations and calculations were done using statistical package S-Plus 2000 software.
Published in 2006.
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## Citation Context (1)

• ...Large dfs is one of the major issues with MLAS. To deal with this problem, we propose a PLS-based MLAS approach, while avoiding large dfs. Simulation study based on real data from the HapMap project suggests that our PLS-based MLAS generally outperformed other three popular MLAS approaches under various scenarios investigated in this study. PLS is suitable to handle the data with many independent variables as well as multicollinearity among the variables ...

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## Citations (2)

### Multilocus Association Testing of Quantitative Traits Based on Partial Least-Squares Analysis

Journal: PLOS One , vol. 6, no. 2, 2011