Model selection in regression linear: A simulation based on akaike's information criterion

Abstract

Akaike's Information Criterion (AIC) was firstly annunced by Akaike in 1971. In linear regression modelling, AIC is proposed as a model selection criterion since it estimates the quality of each model relative to other models. In this paper we domonstrate the use of AIC criterion to estimate p, the number of selected varibles in regression linear model through a simulation study. We simulate two particular cases, namely orthogonal and non - orthogonal cases. The orthogonal case is run where there is totally no correlation between any independent variable and one dependent variable, whereas for the the orthogonal case is run where there is a correlation between some independent variables and one dependent variable. The simulation results are used to investigate of the overestimate number of independent variables selected in the model for two cases. Although the two cases produce the oversetimate number ofindependent variables, most of the time the orthogonal case still provide less overestimate of independent variables than the non orthogonal case.