A heuristic approach to combat multicollinearity in least trimmed squares regression analysis

Roozbeh, Mahdi; Babaie-Kafaki, Saman; Sadigh, Alireza Naeimi

doi:10.1016/j.apm.2017.11.011

Cited by 23 publications

(21 citation statements)

References 17 publications

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“…A heuristic optimization problem based on a penalization scheme to combat outliers and multicollinearity problems. In a recent attempt to overcome the defects of the ridge approach, Roozbeh et al [30] dealt with a modification on the model (3) by embedding a multiple of κ(X ZX) on the cost function of (3) as follows:…”

Section: 2mentioning

confidence: 99%

“…As known, metaheuristic algorithms have attracted special attention in developing efficiently robust computational procedures for solving a vast variety of such problems [38,24]. These nature-inspired methods are so popular since their softwares can be flexibly reused and also, they can efficiently solve complicated problems even in large scale cases [30,8,38].…”

Section: κ(A)mentioning

confidence: 99%

“…This work is organized as follows. In Section 2, we describe some preliminaries in the sense of reviewing the ridge LTS approach and a recent nonlinear integer programming model proposed by Roozbeh et al [30], both being capable to dominate outliers and multicollinearity synchronously. Then, in Section 3 we propose two extended versions of the main model of [30] and discuss how the metaheuristic algorithms can be effectively used to compute the related estimators.…”

mentioning

confidence: 99%

“…In Section 2, we describe some preliminaries in the sense of reviewing the ridge LTS approach and a recent nonlinear integer programming model proposed by Roozbeh et al [30], both being capable to dominate outliers and multicollinearity synchronously. Then, in Section 3 we propose two extended versions of the main model of [30] and discuss how the metaheuristic algorithms can be effectively used to compute the related estimators. To illustrate efficiency of the proposed estimators in real applications, in Section 4 we perform some numerical tests on a bridge construction data, an electricity consumption data and a larger data set of determinants of wages.…”

mentioning

confidence: 99%

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Two penalized mixed–integer nonlinear programming approaches to tackle multicollinearity and outliers effects in linear regression models

Roozbeh¹,

Babaie-Kafaki²,

Aminifard³

2021

JIMO

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In classical regression analysis, the ordinary least-squares estimation is the best strategy when the essential assumptions such as normality and independency to the error terms as well as ignorable multicollinearity in the covariates are met. However, if one of these assumptions is violated, then the results may be misleading. Especially, outliers violate the assumption of normally distributed residuals in the least-squares regression. In this situation, robust estimators are widely used because of their lack of sensitivity to outlying data points. Multicollinearity is another common problem in multiple regression models with inappropriate effects on the least-squares estimators. So, it is of great importance to use the estimation methods provided to tackle the mentioned problems. As known, robust regressions are among the popular methods for analyzing the data that are contaminated with outliers. In this guideline, here we suggest two mixed-integer nonlinear optimization models which their solutions can be considered as appropriate estimators when the outliers and multicollinearity simultaneously appear in the data set. Capable to be effectively solved by metaheuristic algorithms, the models are designed based on penalization schemes with the ability of down-weighting or ignoring unusual data and multicollinearity effects. We establish that our models are computationally advantageous in the perspective of the flop count. We also deal with a robust ridge methodology. Finally, three real data sets are analyzed to examine performance of the proposed methods.

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Section: 2mentioning

confidence: 99%

Section: κ(A)mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Two penalized mixed–integer nonlinear programming approaches to tackle multicollinearity and outliers effects in linear regression models

Roozbeh¹,

Babaie-Kafaki²,

Aminifard³

2021

JIMO

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“…Hu [20] introduced a ridge estimator by the parametric component β. Liu et al [8] introduced a PCR estimator in partially linear models. For more references, one can refer to Roozbeh [21], Roozbeh et al [22], Akdeniz and Roozbeh [23], Roozbeh et al [24], Roozbeh and Hanzah [25], and Wei and Wang [26].…”

Section: Introductionmentioning

confidence: 99%

New Restricted Liu Estimator in a Partially Linear Model

2020

Discrete Dynamics in Nature and Society

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Selection of Optimal Regression-like Equations for Circular Regression Model via Mallows’ $$C_p$$ and AIC Criteria

Alshqaq

Abuzaid²,

Ahmadini³

2023

Iran J Sci

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A heuristic approach to combat multicollinearity in least trimmed squares regression analysis

Cited by 23 publications

References 17 publications

Two penalized mixed–integer nonlinear programming approaches to tackle multicollinearity and outliers effects in linear regression models

Two penalized mixed–integer nonlinear programming approaches to tackle multicollinearity and outliers effects in linear regression models

New Restricted Liu Estimator in a Partially Linear Model

Selection of Optimal Regression-like Equations for Circular Regression Model via Mallows’ $$C_p$$ and AIC Criteria

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