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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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