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 Elas

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