Variable selection in linear regression analysis with alternative Bayesian information criteria using differential evaluation algorithm

ABSTRACT

In statistical analysis, one of the most important subjects is to select relevant exploratory variables that perfectly explain the dependent variable. Variable selection methods are usually performed within regression analysis. Variable selection is implemented so as to minimize the information criteria (IC) in regression models. Information criteria directly affect the power of prediction and the estimation of selected models. There are numerous information criteria in literature such as Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC). These criteria are modified for to improve the performance of the selected models. BIC is extended with alternative modifications towards the usage of prior and information matrix. Information matrix-based BIC (IBIC) and scaled unit information prior BIC (SPBIC) are efficient criteria for this modification. In this article, we proposed a combination to perform variable selection via differential evolution (DE) algorithm for minimizing IBIC and SPBIC in linear regression analysis. We concluded that these alternative criteria are very useful for variable selection. We also illustrated the efficiency of this combination with various simulation and application studies.

KEYWORDS:

• Differential evolution algorithm
• Information criteria
• Linear regression
• Optimization
• Variable selection

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J05
• 80M50