A proposed Penalty Method for Processing High-Dimensional data in a Factorial Experiment (2 4 ) with two Replication.

Abstract

Abstract: In this paper, a method is proposed to model the mathematical model of a factorial experiment (24) applied in a complete random design suffering from high-dimensional data to a multiple regression model using the general linear model where the matrix (X) contains (81) columns and (32) rows, The columns represent the effect of the levels of each factor and the effect of the interaction between the levels of these factors in addition to the effect of the general arithmetic mean, and the rows represent the number of experiment observations (sample size), then the selection of factors and interactions of important factors using the penalty methods (Lasso, adaptive lasso) and the proposed method on the lasso adaptive weight It was compared with the methods mentioned . A simulation study are conducted to investigate the performance of the proposed method. We employed the mean square errors, R-square, Adjusted R-square and Mean absolute deviation to select the best model and the results show that the proposed method using the lasso adaptive weight variable selection performs well.