COMPARISM OF THE PENALIZED REGRESSION TECHNIQUES WITH CLASSICAL LEAST SQURES IN MINIMIZING THE EFFECT OF MULTICOLLINEARITY
COMPARISM OF THE PENALIZED REGRESSION TECHNIQUES WITH CLASSICAL LEAST SQURES IN MINIMIZING THE EFFECT OF MULTICOLLINEARITY
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Date
2018-06
Authors
JOHNSON, Moses
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Abstract
Abstract
A penalized regression techniques which is a variable selectionhas been developed specifically to eliminate the problem of multicollinearity and also reduce the flaws inherent in the prediction accuracy of the classical ordinary least squares (OLS) regression technique. In this dissertation, we focus on the numerical study of four penalized regression methods. A diabetes dataset was used to compare four of these well-known techniques, namely: Least Absolute Shrinkage Selection Operator (LASSO), Smoothly Clipped Absolute Deviation(SCAD) and Correlation Adjusted Elastic Net (CAEN) and Elastic Net (EN). The whole paths of results (in λ) for the LASSO, SCAD and CAEN models were calculated using the path wise Cyclic Coordinate Descent (CCD) algorithms– in glmnetin R. We used 10-fold cross validation (CV) within glmnetto entirely search for the optimal λ. Regularized profile plots of the coefficient paths for the three methods were also shown. Predictive accuracy was also assessed using the mean squared error (MSE) and the penalized regression models were able to produce feasible and efficient models capable of capturing the linearity in the data than the ordinary least squares model.Since there are lots of variables in many survival data analysis problems, SCAD can also be applied to survival data.After thorough analysis it was observed that SCAD generates a less complex model with a minimum mean square error (MSE) than the three penalized regression compared namely: Least Absolute Shrinkage Selection Operator (LASSO), Elastic Net (EN) and Correlation Adjusted Elastic Net (CAEN).
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A DISSERTATION SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTER DEGREE IN STATISTICS.
Keywords
COMPARISM,, PENALIZED REGRESSION TECHNIQUES,, CLASSICAL LEAST SQURES,, MINIMIZING,, EFFECT,, MULTICOLLINEARITY