Emre Dünder

Variable selection in gamma regression models via artificial bee colony algorithm

ABSTRACT Variable selection is an important task in regression analysis. Performance of the statistical model highly depends on the determination of the subset of predictors. There are several methods to select most relevant variables to construct a good model. However in practice, the dependent variable may have positive continuous values and not normally distributed. In such situations, gamma distribution is more suitable than normal for building a regression model. This paper introduces an heuristic approach to perform variable selection using artificial bee colony optimization for gamma regression models. We evaluated the proposed method against with classical selection methods such as backward and stepwise. Both simulation studies and real data set examples proved the accuracy of our selection procedure.

Energy performance evaluation of OECD countries using Bayesian stochastic frontier analysis and Bayesian network classifiers

ABSTRACT More recently a large amount of interest has been devoted to the use of Bayesian methods for deriving parameter estimates of the stochastic frontier analysis. Bayesian stochastic frontier analysis (BSFA) seems to be a useful method to assess the efficiency in energy sector. However, BSFA results do not expose the multiple relationships between input and output variables and energy efficiency. This study proposes a framework to make inferences about BSFA efficiencies, recognizing the underlying relationships between variables and efficiency, using Bayesian network (BN) approach. BN classifiers are proposed as a method to analyze the results obtained from BSFA.

Particle swarm optimization-based variable selection in Poisson regression analysis via information complexity-type criteria

ABSTRACT Modeling of count responses is widely performed via Poisson regression models. This paper covers the problem of variable selection in Poisson regression analysis. The basic emphasis of this paper is to present the usefulness of information complexity-based criteria for Poisson regression. Particle swarm optimization (PSO) algorithm was adopted to minimize the information criteria. A real dataset example and two simulation studies were conducted for highly collinear and lowly correlated datasets. Results demonstrate the capability of information complexity-type criteria. According to the results, information complexity-type criteria can be effectively used instead of classical criteria in count data modeling via the PSO algorithm.

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.

Subset selection in quantile regression analysis via alternative Bayesian information criteria and heuristic optimization

ABSTRACT Subset selection is an extensively studied problem in statistical learning. Especially it becomes popular for regression analysis. This problem has considerable attention for generalized linear models as well as other types of regression methods. Quantile regression is one of the most used types of regression method. In this article, we consider subset selection problem for quantile regression analysis with adopting some recent Bayesian information criteria. We also utilized heuristic optimization during selection process. Simulation and real data application results demonstrate the capability of the mentioned information criteria. According to results, these information criteria can determine the true models effectively in quantile regression models.