Using multivariate adaptive regression splines to estimate pollution in soil

Kilinc, Betul Kan; Malkoc, Semra; Koparal, A. Savas; Yazici, Berna

International Journal of Advanced and Applied Sciences

Int. j. adv. appl. sci.

EISSN: 2313-3724

Print ISSN: 2313-626X

Volume 4, Issue 2 (February 2017), Pages: 10-16

Title: Using multivariate adaptive regression splines to estimate pollution in soil

Author(s): Betul Kan Kilinc ^1, *, Semra Malkoc ², A. Savas Koparal ², Berna Yazici ¹

Affiliation(s):

¹Department of Statistics, Science Faculty, Anadolu University, 26470, Eskişehir, Turkey
²Applied Research Centre for Environmental Problems, Anadolu University, 26555 Eskişehir, Turkey

https://doi.org/10.21833/ijaas.2017.02.002

Full Text - PDF XML

Abstract:

Heavy metal pollution is one of the main factors of the traffic pollution. The public authorities have been monitoring the concentration of heavy metal by means of sampling stations. This paper describes the response surface models and an intelligent regression algorithm, multivariate adaptive regression splines (MARS) models to data collected from soil at the stations where there were high density of buildings, roads, traffic and tramways. The model variables included the number of car and tramways and the concentration levels of Cadmium (Cd), Zinc (Zn) and Lead (Pb), at depth of 0-100mm. The objective of this study was to apply MARS to analyze the model output when there are a few numbers of design points. Several MARS models developed to simulate the concentration of each heavy metal. The performance of MARS was compared to that of response surface methodology (RSM) using 1st and 2nd order response surface models with respect to the accuracy metrics; root mean square error and adjusted R2. The results showed that MARS models were successful in goodness of fit, suitable and also reliable as compared to the RSM models. Additionally, use of MARS in selection of the variables indicating great contribution on the response was effective.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Response surface, Piecewise regression, Regression spline, Heavy metal

Article History: Received 16 September 2016, Received in revised form 17 November 2016, Accepted 10 December 2016

Digital Object Identifier:

https://doi.org/10.21833/ijaas.2017.02.002

Citation:

Kilinc BK, Malkoc S, Koparal AS, Yazici B (2017). Using multivariate adaptive regression splines to estimate pollution in soil. International Journal of Advanced and Applied Sciences, 4(2): 10-16

http://www.science-gate.com/IJAAS/V4I2/Kilinc.html

References:

Abraham A and Steinberg D (2001). MARS: Still an alien planet in soft computing?. In International Conference on Computational Science, Springer Berlin Heidelberg: 235-244. https://doi.org/10.1007/3-540-45718-6_27

Box GEP and Draper NR (2007). Response surfaces, mixtures, and ridge analyses. John Wiley and Sons, New Jersey, USA. https://doi.org/10.1002/0470072768

Cheng W, Zhang X, Wang K, and Dai X (2009). Integrating classification and regression tree (CART) with GIS for assessment of heavy metals pollution. Environmental Monitoring and Assessment, 158(1-4): 419-431. https://doi.org/10.1007/s10661-008-0594-x PMid:19005769

Chung-Chieh Y, Prasher SO, Lacroix R, and Kim SH (2003). A multivariate adaptive regression splines model for simulation of pesticide transport in soils. Biosystems Engineering, 86(1): 9-15. https://doi.org/10.1016/S1537-5110(03)00099-0

Covelo EF, Matías JM, Vega FA, Reigosa MJ, and Andrade ML (2008). A tree regression analysis of factors determining the sorption and retention of heavy metals by soil. Geoderma, 147(1): 75-85. https://doi.org/10.1016/j.geoderma.2008.08.001

Craven P and Wahba G (1978). Smoothing noisy data with spline functions. Numerische Mathematik, 31(4): 377-403. https://doi.org/10.1007/BF01404567

Crino S and Brown DE (2007). Global optimization with multivariate adaptive regression splines. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 37(2): 333-340. https://doi.org/10.1109/TSMCB.2006.883430 PMid:17416161

Fridedman JH (1991). Multivariate adaptive regression splines (with discussion). The Annals of Statistics, 19(1): 79-141.

Govaerts B and Noel J (2005). Analysing the results of a designed experiment when the response is a curve: Methodology and application in metal injection moulding. Quality and Reliability Engineering International, 21(5): 509-520. https://doi.org/10.1002/qre.737

Gruszczynski S (2005). The assessment of variability of the concentration of chromium in soils with the application of neural networks. Polish Journal of Environmental Studies, 14(6): 743-751.

Hastie T, Tibshirani R, and Friedman J (2001). The elements of statistical learning-data mining, inference and prediction. Springer, New York, USA.

Kan B and Yazici B (2009a). Assessment of fuel consumption using factorial experiments, regression trees and MARS. In the 14th WSEAS International Conference on Applied mathematics. World Scientific and Engineering Academy and Society (WSEAS): 196-201.

Kan B and Yazıcı B (2009b). Determining the coordinates of an experimental data set based on multivariate adaptive regression splines. Proceedings of Joint Statistical Meetings Program Committee, Washington, USA: 3098-3104.

Khuri I and Cornell JA (1987). Response Surfaces. Dekker, New York, USA. PMCid:PMC1492823

Lee DJ and Toscas P (2015). Flexible geostatistical modeling and risk assessment analysis of lead concentration levels of residential soil in the Coeur D'Alene River Basin. Environmental and Ecological Statistics, 22(3): 551-570. https://doi.org/10.1007/s10651-015-0310-2

Long A, Zhang H, and Lei Y (2013). Surfactant flushing remediation of toluene contaminated soil: Optimization with response surface methodology and surfactant recovery by selective oxidation with sulfate radicals. Separation and Purification Technology, 118: 612-619. https://doi.org/10.1016/j.seppur.2013.08.001

Martínez-Fernández, D, Bingöl D, and Komárek M (2014). Trace elements and nutrients adsorption onto nano-maghemite in a contaminated-soil solution: a geochemical/statistical approach. Journal of Hazardous Materials, 276: 271-277. https://doi.org/10.1016/j.jhazmat.2014.05.043 PMid:24892777

Nieto PG, Fernández JA, Lasheras FS, de Cos Juez FJ, and Mu-iz CD (2012). A new improved study of cyanotoxins presence from experimental cyanobacteria concentrations in the Trasona reservoir (Northern Spain) using the MARS technique. Science of the Total Environment, 430: 88-92. https://doi.org/10.1016/j.scitotenv.2012.04.068 PMid:22634554

Piedade TC, Souza LCP, and Dieckow J (2014). Three-dimensional data interpolation for environmental purpose: lead in contaminated soils in southern Brazil. Environmental Monitoring and Assessment, 186(9): 5625-5638. https://doi.org/10.1007/s10661-014-3808-4 PMid:24865382

Salford Systems (2010). Overview of MARS methodology. Available online at: https://www.salford-systems.com/resources/whitepapers/113-an-overview-of-mars

Silva C, Pérez P, and Trier A (2001). Statistical modelling and prediction of atmospheric pollution by particulate material: two nonparametric approaches. Environmetrics, 12(2): 147-159. https://doi.org/10.1002/1099-095X(200103)12:2<147::AID-ENV451>3.0.CO;2-3

Steinberg D and Colla PL (1999). MARS™ user guide. Salford Systems, San Diego, California, USA.

Vega FA, Matías JM, Andrade ML, Reigosa MJ, and Covelo EF (2009). Classification and regression trees (CARTs) for modelling the sorption and retention of heavy metals by soil. Journal of Hazardous Materials, 167(1): 615-624. https://doi.org/10.1016/j.jhazmat.2009.01.016 PMid:19200658

Woods D and Lewis S (2006). All‐bias designs for polynomial spline regression models. Australian and New Zealand Journal of Statistics, 48(1): 49-58. https://doi.org/10.1111/j.1467-842X.2006.00424.x

Zhu M, Yao J, Masakorala K, Chandankere R, Chen H, and Ceccanti B (2015). Ultrasound-assisted extraction of pah-contaminated clay soil in the middle Yangtze River basin, China: Optimisation with response surface methodology. Fresenius Environmental Bulletin, 24(10B): 3426-3435.