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D-vine Copula Quantile Regression for a Multidimensional Water Expenditures Analysis: Social and Regional Impacts

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Abstract

Water expenditures variable, as the primary indicator of water consumption, is primordial to analysing and designing water policies. Numerous studies have analyzed water expenditures by considering various factors, including social, spatial, and climate variables predominantly relying on modeling tools often perceived as “black boxes”. In this study, we adopt a different approach, employing D-vine copula quantile regression to scrutinize water expenditures. This method has been proven to be efficient in predicting quantiles for different areas, especially when the normality assumption is inappropriate. Indeed, vine copulas offer the flexibility to select different marginal distributions and a variety of dependence structures. An illustration of the proposed methodology is applied to water consumption in Morocco. The results show different relationships between water expenditures and a set of determinant factors (geographical Area, Sex, and Educational level of the householder), they also show the quantiles’ variability at the regional scale.

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Availability of data and materials

Data are available from the Public Microdata File of the National Survey concerning Household Consumption and Expenditures conducted by the Morrocan High Commission for Planning in 2014 (see Haut Commissariat au Plan (HCP) (2014)). The R code used to generate models, results and graphs is available from the corresponding author upon request.

References

  • Aas K, Czado C, Frigessi A et al (2009) Pair-copula constructions of multiple dependence. Insur Math Econ 44(2):182–198

    Article  MathSciNet  Google Scholar 

  • Arbués F, Garcıa-Valiñas MÁ, Martınez-Espiñeira R (2003) Estimation of residential water demand: a state-of-the-art review. J Socio-Econ 32(1):81–102

    Article  Google Scholar 

  • Bao K, Padsala R, Thrän D et al (2020) Urban water demand simulation in residential and non-residential buildings based on a citygml data model. ISPRS Int J Geo-inf 9(11):642

    Article  Google Scholar 

  • Bedford T, Cooke RM (2001) Probability density decomposition for conditionally dependent random variables modeled by vines. Ann Math Artif Intell 32(1–4):245–268

    Article  MathSciNet  Google Scholar 

  • Bedford T, Cooke RM (2002) Vines: a new graphical model for dependent random variables. Ann Stat 1031–1068

  • Bich-Ngoc N, Teller J (2018) A review of residential water consumption determinants. In: Computational science and its applications–ICCSA 2018: 18th International Conference, Melbourne, VIC, Australia, July 2-5, 2018, Proceedings, Part V 18, Springer, pp 685–696

  • Cheng Z, He J, Liu Y et al (2023) Exploring the spatial structure and impact factors of water use efficiency in China. Environ Impact Assess Rev 103:107258

    Article  Google Scholar 

  • Dalhuisen JM, Florax RJ, De Groot HL et al (2003) Price and income elasticities of residential water demand: a meta-analysis. Land Econ 79(2):292–308

    Article  Google Scholar 

  • Deger IH, Esıt M, Yuce MI (2023) Univariate and bivariate hydrological drought frequency analysis by copula functions. Water Resour Manag 37(12):4881–4907

    Article  Google Scholar 

  • del Villar A, Melgarejo J (2020) Prospective models for water service demand and price analyses. Water 12(6):1613

    Article  Google Scholar 

  • Dissmann J, Brechmann EC, Czado C et al (2013) Selecting and estimating regular vine copulae and application to financial returns. Comput Stat Data Anal 59:52–69

    Article  MathSciNet  Google Scholar 

  • El Adlouni S (2018) Quantile regression c-vine copula model for spatial extremes. Nat Hazards 94(1):299–317

    Article  Google Scholar 

  • El Hannoun W, El Adlouni SE, Zoglat A (2021) Vine-copula-based quantile regression for cascade reservoirs management. Water 13(7):964

    Article  Google Scholar 

  • El Hannoun W, Boukili Makhoukhi A, Zoglat A et al (2023) Intensity-duration-frequency curves for dependent datasets. Water 15(14):2641

    Article  Google Scholar 

  • Guercio R, Magini R, Pallavicini I (1970) Instantaneous residential water demand as stochastic point process. WIT Trans Ecol Environ 48

  • Haut Commissariat au Plan (HCP) (2014) Enquête Nationale sur la Consommation et les Dépenses des Ménages (ENCDM)

  • Kostas B, Chrysostomos S (2006) Estimating urban residential water demand determinants and forecasting water demand for athens metropolitan area, 2000-2010. South-Eastern Europe Journal of Economics 4(1)

  • Kraus D, Czado C (2017) D-vine copula based quantile regression. Comput Stat Data Anal 110:1–18

    Article  MathSciNet  Google Scholar 

  • Latif S, Simonovic SP (2023) Trivariate probabilistic assessments of the compound flooding events using the 3-d fully nested archimedean (fna) copula in the semiparametric distribution setting. Water Resour Manag 37(4):1641–1693

    Article  Google Scholar 

  • Ma JR, NR C (2023) Application of copulas in hydrometeorological drought risk analysis under climate change scenarios-a case study. Water Resour Manag 37(14):5399–5429

  • Mangalekar R, Gumaste K (2021) Residential water demand modelling and hydraulic reliability in design of building water supply systems: a review. Water Supply 21(4):1385–1397

    Article  Google Scholar 

  • Motevali Bashi Naeini E, Akhoond-Ali AM, Radmanesh F et al (2021) Comparison of the calculated drought return periods using tri-variate and bivariate copula functions under climate change condition. Water Resour Manag 35:4855–4875

    Article  Google Scholar 

  • Mu X, Whittington D, Briscoe J (1990) Modeling village water demand behavior: a discrete choice approach. Water Resour Res 26(4):521–529

    Article  ADS  Google Scholar 

  • Nagler T, Kraus D (2019) vinereg: D-vine quantile regression. R package version 070

  • Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 23(3):470–472

    Article  MathSciNet  Google Scholar 

  • Schepsmeier U (2015) Efficient information based goodness-of-fit tests for vine copula models with fixed margins: a comprehensive review. J Multivar Anal 138:34–52

    Article  MathSciNet  Google Scholar 

  • Schleich J, Hillenbrand T (2009) Determinants of residential water demand in germany. Ecol Econ 68(6):1756–1769

    Article  Google Scholar 

  • Sklar M (1959) Fonctions de répartition à n dimensions et leurs marges. In: Annales de l’ISUP, pp 229–231

  • Taher S, Alsaati A (2002) Cross sectional analysis of residential water consumption in the city of riyadh. Wat Eng Res Int J KWRA 3(4):269–278

    Google Scholar 

  • Tepegjozova M, Zhou J, Claeskens G et al (2022) Nonparametric c-and d-vine-based quantile regression. Depend Model 10(1):1–21

    Article  MathSciNet  Google Scholar 

  • Termes-Rife M, Bernardo V (2015) Water demand models. University of Barcelona

  • Worthington AC, Hoffman M (2008) An empirical survey of residential water demand modelling. J Econ Surv 22(5):842–871

    Article  Google Scholar 

  • Worthington A, Hoffman M (2007) A state of the art review of residential water demand modelling, School of Accounting & Finance, University of Wollongong. Tech. rep., Working Paper 6

  • Xie K, He Y, Kim JS et al (2023) Assessment of the joint impact of rainfall characteristics on urban flooding and resilience using the copula method. Water Resour Manag 37(4):1765–1784

    Article  Google Scholar 

  • Zhao Y, Guo L, Li Y et al (2023) Revealing the driving factors for structure changes of regional water consumption: an empirical study of the middle route project of the south-to-north water diversion in China. Environ Dev Sustain 1–24

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Acknowledgements

The authors would like to thank the Editor and the Reviewers for their time and comments that helped improve the manuscript. The authors would also like to thank Samuel Leclerc, a student at the Université de Moncton, for the English language editing.

Funding

This research was supported by the PPR2 8/2016 program, a Moroccan government program to support scientific research.

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Authors and Affiliations

  1. Laboratory of Mathematics, Statistics and Applications, Faculty of Sciences, Mohammed V University in Rabat, Rabat, 1014, Morocco

    El Hannoun Wafaa & Zoglat Abdelhak

  2. Mohammed V University in Rabat, Rabat, Morocco

    Ezzahid ElHadj

  3. Department of Mathematics and Statistics, Université de Moncton, Moncton, NB, E1A 3E9, Canada

    El Adlouni Salah-Eddine

Authors
  1. El Hannoun Wafaa
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  2. Zoglat Abdelhak
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  3. Ezzahid ElHadj
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  4. El Adlouni Salah-Eddine
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Contributions

W.E.H.: Conceptualization, Methodology, Investigation, Data curation, Formal Analysis, Writing - Original Draft. A.Z.: Conceptualization, Methodology, Writing & Review. E. E.: Conceptualization, Methodology, Writing & Review. S.-E.E.A.: Methodology, Writing & Review.

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Correspondence to El Hannoun Wafaa.

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Wafaa, E.H., Abdelhak, Z., ElHadj, E. et al. D-vine Copula Quantile Regression for a Multidimensional Water Expenditures Analysis: Social and Regional Impacts. Water Resour Manage (2024). https://doi.org/10.1007/s11269-024-03813-z

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  • DOI: https://doi.org/10.1007/s11269-024-03813-z

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