Tackling multicollinearity in greenhouse gas emission drivers: Ridge and Liu-Based mixed model approaches
DOI:
https://doi.org/10.35208/ert.1649373Keywords:
Environmental statistics, greenhouse gas emissions, linear mixed models, Liu prediction, multicollinearity, Ridge predictionAbstract
Greenhouse gases (GHGs) such as water vapor (H₂O), carbon dioxide (CO₂), nitrous oxide (N₂O), methane (CH₄), ozone (O₃), and other harmful gases are the major drivers of global warming, as they absorb solar radiation and trap heat in the atmosphere. Identifying the factors that influence GHG emissions is therefore crucial for tackling climate change, safeguarding public health, and ensuring environmental sustainability. This study examines the role of six industrial sectors—agriculture, forestry and fishing (AFF); manufacture of food, beverages and tobacco (FBT); manufacture of paper and paper products (PPP); manufacture of chemicals and chemical products (CCP); water supply, sewerage, waste management and remediation (WSR); and transportation and storage (TS)—in shaping GHG emissions across 17 Eurostat countries between 2010 and 2021. To address the issue of multicollinearity among sectoral variables, we apply ridge and Liu estimators within a linear mixed model framework. The findings advance statistical methodologies for environmental data analysis and provide insights into the primary industrial drivers of GHG emissions. By highlighting the most influential industrial sectors and demonstrating the advantages of ridge and Liu estimators in handling multicollinearity, this study offers a pathway for more accurate climate modeling and evidence-based policymaking. These approaches can support the design of targeted mitigation strategies and guide future climate analytics toward more reliable and interpretable outcomes.
Downloads
References
[1]. J. C. Pinheiro, and D. M. Bates, “Mixed-effects models in S and S-PLUS (2nd ed.),” Springer-Verlag, New York. 2000.
[2]. A. F. Zuur, E. N. Ieno, N. J. Walker, A. A. Saveliev, and G. M. Smith, “Mixed effects models and extensions in ecology with R,” Springer-Verlag, New York. 2009.
[3]. C. R. Henderson, “Estimation of genetic parameters (abstract),” Annals of Mathematical Statistics, Vol. 21, pp. 309–310, 1950.
[4]. C. R. Henderson, O. Kempthorne, S. R. Searle, and C. N. von Krosig, “Estimation of environmental and genetic trends from records subject to culling,” Biometrics, Vol. 15, pp. 192–218, 1959.
[5]. X. Q. Liu, and P. Hu, “General ridge predictors in a mixed linear model,” A Journal of Theoretical and Applied Statistics, Vol. 47, pp. 363–378, 2013.
[6]. M. N. Eliot, J. Ferguson, M. P. Reilly, and A. S. Foulkes, "Ridge regression for longitudinal biomarker data," International Journal of Biostatistics, Vol. 7, pp. 1–11, 2011.
[7]. A. E. Hoerl and R. W. Kennard, "Ridge regression: Biased estimation for nonorthogonal problems," Technometrics, Vol. 12, pp. 55–67, 1970.
[8]. M. R. Özkale, and F. Can, “An evaluation of ridge estimator in linear mixed models: an example from kidney failure data,” Journal of Applied Statistics, Vol. 44, pp. 2251–2269, 2017.
[9]. K. Liu, "A new class of biased estimate in linear regression," Communications in Statistics - Theory and Methods, Vol. 22, pp. 393–402, 1993.
[10]. S. Kaçıranlar, S. Sakallıoğlu, F. Akdeniz, G. P. H. Styan, and H. J. Werner, "A new biased estimator in linear regression and a detailed analysis of the widely analyzed dataset on Portland Cement," Sankhya: The Indian Journal of Statistics, Vol. 61B, pp. 443–459, 1999.
[11]. B. F. Swindel, "Good estimators based on prior information," Communications in Statistics - Theory and Methods, Vol. 5, pp. 1065–1075, 1976.
[12]. M. R. Özkale, and S. Kaçıranlar, "The restricted and unrestricted two-parameter estimators," Communications in Statistics - Theory and Methods, Vol. 36, pp. 2707–2725, 2007.
[13]. M. R. Özkale, and Ö. Kuran, "A further prediction method in linear mixed models: Liu prediction," Communications in Statistics - Simulation and Computation, Vol. 49(12), pp. 3171–3195, 2020.
[14]. M. R. Özkale, and Ö. Kuran, “Adaptation of the jackknifed ridge methods to the linear mixed models,” Journal of Statistical Computation and Simulation, Vol. 89(18), pp. 3413-3452, 2019.
[15]. Ö. Kuran, "Generalized Kibria-Lukman prediction approximation in linear mixed models," Fundamentals of Contemporary Mathematical Sciences, Vol. 5(1), pp. 25-35, 2024.
[16]. Ö. Kuran, "Mean square error performance of the modified jackknifed ridge predictors in the linear mixed models," Erciyes University Journal of Institue of Science and Technology, Vol. 36(3), pp. 400-407, 2020.
[17]. Ö. Kuran, and M. R. Özkale, “Improvement of mixed predictors in linear mixed models,” Journal of Applied Statistics, Vol. 48(5), pp. 924-942, 2021.
[18]. Ö. Kuran, “The r-d class predictions in linear mixed models,” Journal of Inverse and Ill-Posed Problems, Vol. 29(4), pp. 477–498, 2021.
[19]. H. Yang, H. Ye, and K. Xue, “A further study of predictions in linear mixed models,” Communications in Statistics - Theory and Methods, Vol. 43, pp. 4241–4252, 2014.
[20]. L. N. Pereira, and P. S. Coelho, “A small area predictor under area-level linear mixed models with restrictions,” Communications in Statistics - Theory and Methods, Vol. 41, pp. 2524–2544, 2012.
[21]. G. K. Robinson, “That BLUP is a good thing: the estimation of random effects (with discussion),” Statistical Science, Vol. 6, pp. 15–51, 1991.
[22]. F. Štulajter, “Predictions in nonlinear regression models,” Acta Mathematica Universitatis Comenianae, Vol. 66, pp. 71–81, 1997.
[23]. Eurostat, “Air emissions accounts by NACE Rev. 2 activity,” Retrieved from https://ec.europa.eu/eurostat/databrowser/view/env_ac_ainah_r2__custom_7965996/default/table?lang=en, 2023.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Environmental Research and Technology

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
All articles in Environmental Research and Technology (ERT) are published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
This license allows others to copy, distribute, and adapt the work for non-commercial purposes only, provided that proper credit is given to the original authors and to the journal.



