Employing Some Penalized Methods for Selecting the Main Effects and Interaction in Factorial Design via Simulation

Abstract

The well-known scientific research "factorial experiments design" studied the effect of the factors, the levels, and the interaction of levels of the underlying phenomenon. Also, factorial experiments design aims to study the reaction of the experimental units to the interested factors. Variable section procedure in the study of the factorial experiments design it is of interest to researchers working in the field of designing factorial experiments. Design regression model with large number of levels and its interactions produced overfitted model, so removing the relevant levels of the designing factorial experiments are very important to yield the more accurate estimated model. This paper focused on variable selection regularization methods to find the sparse solution of the interested parameters. Such as (lasso, length, Elastic net, and  group lasso). Simulation study have conducted, two simulation examples have conducted to examine the ability of the above variable selection method in factorial experiments, and the results show that the group lasso and followed by elastic net are the best methods in term of variable selection method because it give the sparse solution with smallest EER and MSE values as measures of estimate quality.