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Next issue: volume 44 (2), July-December 2020
Discrete generalized half normal distribution and its applications in quantile regression
Diego I. Gallardo, Emilio Gómez-Déniz and Héctor W. Gómez
A simheuristic algorithm for time-dependent waste collection management with stochastic travel times
Aljoscha Gruler, Antoni Perez-Navarro, Laura Calvet and Angel A. Juan
Why simheuristics? Benefits, limitations, and best practices when combining metaheuristics with simulation
Manuel Chica, Angel A. Juan, Christopher Bayliss, Oscar Cordon and W. David Kelton
Current issue: volume 44 (1), January-June 2020
Small area estimation of additive parameters under unit-level generalized linear mixed models
Tomáš Hobza, Yolanda Marhuenda and Domingo Morales
Abstract: Average incomes and poverty proportions are additive parameters obtained as averages of a given function of an income variable. As the variable income has an asymmetric distribution, it is not properly modelled via normal distributions. When dealing with this type of variable, a first option is to apply transformations that approximate normality. A second option is to use nonsymmetric distributions from the exponential family. This paper proposes unit-level generalized linear mixed models for modelling asymmetric positive variables and for deriving three types of predictors of small area additive parameters, called empirical best, marginal and plug-in. The parameters of the introduced model are estimated by applying the maximum likelihood method to the Laplace approximation of the likelihood. The mean squared errors of the predictors are estimated by parametric bootstrap. The introduced methodology is applied and illustrated under unit-level gamma mixed models. Some simulation experiments are carried out to study the behaviour of the fitting algorithm, the small area predictors and the bootstrap estimator of the mean squared errors. By using data of the Spanish living condition survey of 2013, an application to the estimation of average incomes and poverty proportions in counties of the region of Valencia is given.
Keywords: Average income, poverty proportion, generalized linear mixed models, empirical best predictor, mean squared error, bootstrap
Finding archetypal patterns for binary questionnaires
Ismael Cabero and Irene Epifanio
Abstract: Archetypal analysis is an exploratory tool that explains a set of observations as mixtures of pure (extreme) patterns. If the patterns are actual observations of the sample, we refer to them as archetypoids. For the first time, we propose to use archetypoid analysis for binary observations. This tool can contribute to the understanding of a binary data set, as in the multivariate case. We illustrate the advantages of the proposed methodology in a simulation study and two applications, one exploring objects (rows) and the other exploring items (columns). One is related to determining student skill set profiles and the other to describing item response functions.
Keywords: Dichotomous item test, archetypal analysis, functional data analysis, item response theory, skill profile
Integer constraints for enhancing interpretability in linear regression
Emilio Carrizosa, Alba V. Olivares-Nadal and Pepa Ramírez-Cobo
Abstract: One of the main challenges researchers face is to identify the most relevant features in a prediction model. As a consequence, many regularized methods seeking sparsity have flourished. Although sparse, their solutions may not be interpretable in the presence of spurious coefficients and correlated features. In this paper we aim to enhance interpretability in linear regression in presence of multicollinearity by: (i) forcing the sign of the estimated coefficients to be consistent with the sign of the correlations between predictors, and (ii) avoiding spurious coefficients so that only significant features are represented in the model. This will be addressed by modelling constraints and adding them to an optimization problem expressing some estimation procedure such as ordinary least squares or the lasso. The so-obtained constrained regression models will become Mixed Integer Quadratic Problems. The numerical experiments carried out on real and simulated datasets show that tightening the search space of some standard linear regression models by adding the constraints modelling (i) and/or (ii) help to improve the sparsity and interpretability of the solutions with competitive predictive quality.
Keywords: Linear regression, Multicollinearity, Sparsity, Cardinality constraint, Mixed Integer Non Linear Programming
Modelling count data using the logratio-normal-multinomial distribution
Marc Comas-Cufí, Josep Antoni Martín-Fernández, Glòria Mateu-Figueras and Javier Palarea-Albaladejo
Abstract: The logratio-normal-multinomial distribution is a count data model resulting from compounding a multinomial distribution for the counts with a multivariate logratio-normal distribution for the multinomial event probabilities. However, the logratio-normal-multinomial probability mass function does not admit a closed form expression and, consequently, numerical approximation is required for parameter estimation. In this work, different estimation approaches are introduced and evaluated. We concluded that estimation based on a quasi-Monte Carlo Expectation-Maximisation algorithm provides the best overall results. Building on this, the performances of the Dirichlet-multinomial and logratio-normal-multinomial models are compared through a number of examples using simulated and real count data.
Keywords: Count data, Compound probability distribution, Dirichlet Multinomial, Logratio coordinates, Monte Carlo method, Simplex
Bartlett and Bartlett-type corrections for censored data from a Weibull distribution
Tiago M. Magalhães and Diego I. Gallardo
Abstract: In this paper, we obtain the Bartlett factor for the likelihood ratio statistic and the Bartlett-type correction factor for the score and gradient test in censored data from a Weibull distribution. The expressions derived are simple, we only have to define a few matrices. We conduct an extensive Monte Carlo study to evaluate the performance of the corrected tests in small sample sizes and we show how they improve the original versions. Finally, we apply the results to a real data set with a small sample size illustrating that conclusions about the regressors could be different if corrections were not applied to the three mentioned classical statistics for the hypothesis test.
Keywords: Bartlett correction, censored data, Weibull distribution, chi-squared distribution, maximum likelihood estimates, type I and II censoring
Green hybrid fleets using electric vehicles: solving the heterogeneous vehicle routing problem with multiple driving ranges and loading capacities
Sara Hatami, Majid Eskandarpour, Manuel Chica, Angel A. Juan and Djamila Ouelhadj
Abstract: The introduction of Electric Vehicles (EVs) in modern fleets facilitates green road transportation. However, the driving ranges of EVs are limited by the duration of their batteries, which arise new operational challenges. Hybrid fleets of gas and EVs might be heterogeneous both in loading capacities as well as in driving-range capabilities,whichmakes the design of efficient routing plans a difficult task. In this paper, we propose a newMulti-Round IteratedGreedy (MRIG) metaheuristic to solve the Heterogeneous Vehicle Routing Problem with Multiple Driving ranges and loading capacities (HeVRPMD). MRIG uses a successive approximations method to offer the decision maker a set of alternative fleet configurations,with different distance-based costs and green levels. The numerical experiments show that MRIG is able to outperform previous works dealing with the homogeneous version of the problem, which assumes the same loading capacity for all vehicles in the fleet. The numerical experiments also confirm that the proposed MRIG approach extends previous works by solving a more realistic HeVRPMD and provides the decision-maker with fleets with higher green levels.
Keywords: Vehicle Routing Problem, Electric Vehicles, Heterogeneous Fleet, Multiple Driving Ranges. Iterated Greedy heuristic, Successive Approximations Method
Bayesian structured antedependence model proposals for longitudinal data
Edwin Castillo-Carreno, Edilberto Cepeda-Cuervo and Vicente Núñez-Antón
Abstract: An important problem in Statistics is the study of longitudinal data taking into account the effect of other explanatory variables, such as treatments and time and, simultaneously, the incorporation into the model of the time dependence between observations on the same individual. The latter is specially relevant in the case of nonstationary correlations, and nonconstant variances for the different time point at which measurements are taken. Antedependence models constitute a well known commonly used set of models that can accommodate this behaviour. These covariance models can include too many parameters and estimation can be a complicated optimization problem requiring the use of complex algorithms and programming. In this paper, a new Bayesian approach to analyse longitudinal data within the context of antedependence models is proposed. This innovative approach takes into account the possibility of having nonstationary correlations and variances, and proposes a robust and computationally efficient estimation method for this type of data. We consider the joint modelling of the mean and covariance structures for the general antedependence model, estimating their parameters in a longitudinal data context. Our Bayesian approach is based on a generalization of the Gibbs sampling and Metropolis-Hastings by blocks algorithm, properly adapted to the antedependence models longitudinal data settings. Finally, we illustrate the proposed methodology by analysing several examples where antedependence models have been shown to be useful: the small mice, the speech recognition and the race data sets.
Keywords: Antedependence models, Bayesian methods, Gibbs sampling, Mean-covariance modelling, Nonstationary correlation
On interpretations of tests and effect sizes in regression models with a compositional predictor
Germà Coenders and Vera Pawlowsky-Glahn
Abstract: The inclusion of stakeholder behaviour in Operations Research / Industrial Engineering (OR/IE) models has gained much attention in recent years. Behavioural and cognitive traits of people and groups have been integrated in simulation models (mainly through agent-based approaches) as well as in optimization algorithms. However, especially the influence of relations between different actors in human networks is a broad and interdisciplinary topic that has not yet been fully investigated. This paper analyses, from an OR/IE point of view, the existing literature on behaviour-related factors in human networks. This review covers different application fields, including: supply chain management, public policies in emergency situations, and Internet-based human networks. The review reveals that the methodological approach of choice (either simulation or optimization) is highly dependent on the application area. However, an integrated approach combining simulation and optimization is rarely used. Thus, the paper proposes the hybridization of simulation with optimization as one of the best strategies to incorporate human behaviour in human networks and the resulting uncertainty, randomness, and dynamism in related OR/IE models.
Keywords: Modelling human behaviour, human networks, simulation, optimization, simheuristics