Variable Selection in Count Data Regression Model based on Firefly Algorithm

Zakariya Algamal

doi:10.19139/soic.v7i2.566

Abstract

Variable selection is a very helpful procedure for improving computational speed and prediction accuracy by identifying the most important variables that related to the response variable. Count data regression modeling has received much attention in several science fields in which the Poisson and negative binomial regression models are the most basic models. Firefly algorithm is one of the recently efficient proposed nature-inspired algorithms that can efficiently be employed for variable selection. In this work, firefly algorithm is proposed to perform variable selection for count data regression models. Extensive simulation studies and two real data applications are conducted to evaluate the performance of the proposed method in terms of prediction accuracy and variable selection criteria. Further, its performance is compared with other methods. The results proved the efficiency of our proposed methods and it outperforms other popular methods.

Highlights

In regression modeling, data in the form of counts are usually common
The purpose of this paper is to propose firefly algorithm, which is a swarm intelligence technique, as an alternative variable selection method for use in count data regression model
Based on 500 times of repeating simulation, the averaged mean squared error (MSE), I, and C with their associated standard deviations are listed in Tables 1-6, respectively, for Poisson regression model (PRM) and. It shows from these tables that the Firefly optimization algorithm (FA)-BN method there has a significant improvement where it has a much better average of MSE than those Akaike information criteria (AIC), corrected Akaike information criteria (CAIC), and Bayesian information criteria (BIC) methods

Summary

Introduction

Data in the form of counts are usually common. Count data regression modeling has received much attention in medicine, behavioral sciences, psychology, and econometrics [1, 2, 3, 36]. The naturally inspired algorithms, such as genetic algorithm, particle swarm optimization algorithm, firefly algorithm, and crow search algorithm, have a great attraction and proved their efficiency as variable selection methods [12]. This is because that the main target in variable selection is to minimize the number of selected variables while maintaining the maximum accuracy of prediction, and, they can be considered as optimization problems [13]. The purpose of this paper is to propose firefly algorithm, which is a swarm intelligence technique, as an alternative variable selection method for use in count data regression model. The superiority of the proposed algorithm is proved though different simulation settings and a real data application

Count data regression model

Firefly algorithm

Computational results

Methods

Findings