Should We Account for Network Distances or Anisotropy in the Spatial Estimation of Missing Traffic Data?
DOI:
https://doi.org/10.58922/transportes.v31i1.2822Keywords:
Annual Average Daily Traffic, Ordinary Kriging, Network distances, AnisotropyAbstract
In light of the unavailability of traffic volume data for all road segments, the scientific literature proposes estimating this variable using spatial interpolators. However, most of the methods found use the Euclidean distance between the database points as a proximity measure, in addition to ignoring the anisotropy of the phenomenon. Thus, the objective of the present study was to apply Ordinary Kriging (OK) with network distances and anisotropic OK in traffic volume data on highways in the state of São Paulo (Brazil), comparing its results to the traditional isotropic approach with Euclidean distances. Goodness-of-fit measures confirmed the good performance and better suitability of OK with network distances over the analyses that use Euclidean distances. Addressing the anisotropy of the traffic volume data also helped to improve the results. The proposed method can effectively support estimating traffic volume in segments without flow data.
Downloads
References
Apronti, D.; K. Ksaibati; K. Gerow et al. (2016) Estimating traffic volume on Wyoming low volume roads using linear and logistic regression methods. Journal of Traffic and Transportation Engineering, v. 3, n. 6, p. 493-506. DOI: 10.1016/j.jtte.2016.02.004. DOI: https://doi.org/10.1016/j.jtte.2016.02.004
Box, G.E.P. and D.R. Cox (1964) An analysis of transformations. Journal of the Royal Statistical Society. Series A (General), v. 26, n. 2, p. 211-52. DOI: https://doi.org/10.1111/j.2517-6161.1964.tb00553.x
Carvalho, S.D.P.C.; L.C.E. Rodriguez; L.D. Silva et al. (2015) Predição do volume de árvores integrando Lidar e Geoestatística. Scientia Forestalis, v. 43, n. 107, p. 627-37.
Chi, G. and Y. Zheng (2013) Estimating transport footprint along highways at local levels: a combination of network analysis and kriging methods. International Journal of Sustainable Transportation, v. 7, n. 3, p. 261-73. DOI: 10.1080/15568318.2013.710150. DOI: https://doi.org/10.1080/15568318.2013.710150
Chiles, J. and P. Delfiner (2012) Geostatistics: Modeling Spatial Uncertainty (2nd ed). New Jersey: John Wiley & Sons. DOI: 10.1002/9781118136188. DOI: https://doi.org/10.1002/9781118136188
Cressie, N. and D.M. Hawkins (1980) Robust estimation of the variogram: I. Journal of the International Association for Mathematical Geology, v. 12, n. 2, p. 115-25. DOI: 10.1007/BF01035243. DOI: https://doi.org/10.1007/BF01035243
Cressie, N.A.C. (1993) Statistics for Spatial Data. New Jersey: John Wiley & Sons. DOI: https://doi.org/10.1002/9781119115151
Deutsch, C.V. and A.G. Journel (1998) GSLIB: Geostatistical Software Library and User’s Guide (2nd ed). New York: Oxford University Press.
DNIT (2006) Manual de Estudos de Tráfego. Rio de Janeiro: Departamento Nacional de Infraestrutura de Transportes. Available at: <https://www.gov.br/dnit/pt-br/assuntos/planejamento-e-pesquisa/ipr/coletanea-demanuais/vigentes/723_manual_estudos_trafego.pdf> (accessed 06/03/2023).
Duddu, V.R. and S.S. Pulugurtha (2013) Principle of demographic gravitation to estimate annual average daily traffic: comparison of statistical and neural network models. Journal of Transportation Engineering, v. 139, n. 6, p. 585-95. DOI: 10.1061/(ASCE)TE.1943-5436.0000537. DOI: https://doi.org/10.1061/(ASCE)TE.1943-5436.0000537
Eom, J.K.; M.S. Park; T. Heo et al. (2006) Improving the prediction of annual average daily traffic for nonfreeway facilities by applying a spatial statistical method. Transportation Research Record: Journal of the Transportation Research Board, v. 1968, n. 1, p. 20-9. DOI: 10.1177/0361198106196800103. DOI: https://doi.org/10.1177/0361198106196800103
Eriksson, M. and P.P. Siska (2000) Understanding anisotropy computations. Mathematical Geology, v. 32, n. 6, p. 683-700. DOI: 10.1023/A:1007590322263. DOI: https://doi.org/10.1023/A:1007590322263
Evans, J.S. (2021) _spatialEco_. R package version 1.3-6. Available at: <https://github.com/jeffreyevans/spatialEco> (accessed 06/03/2023).
Gomes, M.M.; C.S. Pitombo; A. Pirdavani et al. (2018) Geostatistical approach to estimate car occupant fatalities in traffic accidents. Revista Brasileira de Cartografia, v. 70, n. 4, p. 1231-56. DOI: 10.14393/rbcv70n4-46140. DOI: https://doi.org/10.14393/rbcv70n4-46140
Goovaerts, P. (2009) Medical geography: a promising field of application for geostatistics. Mathematical Geosciences, v. 41, n. 3, p. 243-64. DOI: 10.1007/s11004-008-9211-3. PMid:19412347. DOI: https://doi.org/10.1007/s11004-008-9211-3
Hollander, Y. and R. Liu (2008) The principles of calibrating traffic microsimulation models. Transportation, v. 35, n. 3, p. 347-62. DOI: 10.1007/s11116-007-9156-2. DOI: https://doi.org/10.1007/s11116-007-9156-2
IBGE (2021) IBGE Cidades. Available at: <https://cidades.ibge.gov.br/brasil/sp/sao-paulo/panorama> (accessed 06/03/2023).
Isaaks, E.H. and R.M. Srivastava (1989) An Introduction to Applied Geostatistics (1st ed). New York: Oxford University Press. Available at: <https://books.google.com.br/books?id=t62mtgAACAAJ> (accessed 06/03/2023).
Kerry, R.; P. Goovaerts; D. Giménez et al. (2016) Investigating geostatistical methods to model within-field yield variability of cranberries for potential management zones. Precision Agriculture, v. 17, n. 3, p. 247-73. DOI: 10.1007/s11119-015-9408-7. DOI: https://doi.org/10.1007/s11119-015-9408-7
Khan, S.M.; S. Islam; M.D.Z. Khan et al. (2018) Development of statewide annual average daily traffic estimation model from short-term counts: a comparative study for South Carolina. Transportation Research Record: Journal of the Transportation Research Board, v. 2672, n. 43, p. 55-64. DOI: 10.1177/0361198118798979. DOI: https://doi.org/10.1177/0361198118798979
Kim, S.; D. Park; T. Heo et al. (2016) Estimating vehicle miles traveled (VMT) in urban areas using regression kriging. Journal of Advanced Transportation, v. 50, n. 5, p. 769-85. DOI: 10.1002/atr.1374. DOI: https://doi.org/10.1002/atr.1374
Klatko, T.J.; T.U. Saeed; M. Volovski et al.(2017) Addressing the local-road VMT estimation problem using spatial interpolation techniques. Journal of Transportation Engineering, Part A: Systems, v. 143, n. 8, p. 4017038. DOI: 10.1061/JTEPBS.0000064. DOI: https://doi.org/10.1061/JTEPBS.0000064
Krige, D.G. (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. Journal of the Southern African Institute of Mining and Metallurgy, v. 52, n. 6, p. 119-39.
Lindner, A. and C.S. Pitombo (2019) Sequential Gaussian simulation as a promising tool in travel demand modeling. Journal of Geovisualization and Spatial Analysis, v. 3, n. 2, p. 15. DOI: 10.1007/s41651-019-0038-x. DOI: https://doi.org/10.1007/s41651-019-0038-x
Marques, S.F. and C.S. Pitombo (2020) Intersecting geostatistics with transport demand modeling: a bibliographic survey. Revista Brasileira de Cartografia, v. 72, p. 1028-50. DOI: 10.14393/rbcv72nespecial50anos-56467. DOI: https://doi.org/10.14393/rbcv72nespecial50anos-56467
Marques, S. de F. and C.S. Pitombo (2021a) Applying multivariate Geostatistics for transit ridership modeling at the bus stop level. Boletim de Ciências Geodésicas, v. 27, n. 2, p. e2021019. DOI: 10.1590/1982-2170-2020-0069. DOI: https://doi.org/10.1590/1982-2170-2020-0069
Marques, S.F. and C.S. Pitombo (2021b) Ridership estimation along bus transit lines based on kriging: comparative analysis between network and euclidean distances. Journal of Geovisualization and Spatial Analysis, v. 5, n. 1, p. 7. DOI: 10.1007/s41651-021-00075-w. DOI: https://doi.org/10.1007/s41651-021-00075-w
Marques, S.F. and C.S. Pitombo (2021c) Spatial modeling of transit ridership along bus lines with overlapping sections. In: Anais do 35o Congresso de Pesquisa e Ensino em Transportes. p. 1568-80. Available at: <https://www.researchgate.net/publication/357517939_SPATIAL_MODELING_OF_TRANSIT_RIDERSHIP_ALONG_BUS_LINES_WITH_OVERLAPPING_SECTIONS> (accessed 06/03/2023).
Matheron, G. (1971) The Theory of Regionalized Variables and its Applications. Paris: Les Cahiers du Centre de Morphologie Mathematique in Fontainebleu.
Mathew, S. and S.S. Pulugurtha (2021) Comparative assessment of geospatial and statistical methods to estimate local road annual average daily traffic. Journal of Transportation Engineering, Part A: Systems, v. 147, n. 7, p. 04021035. DOI: 10.1061/JTEPBS.0000542. DOI: https://doi.org/10.1061/JTEPBS.0000542
Millard, S.P. (2013) EnvStats: an R Package for Environmental Statistics. New York: Springer. DOI: https://doi.org/10.1007/978-1-4614-8456-1
Moran, P.A.P. (1948) The interpretation of statistical maps. Journal of the Royal Statistical Society. Series B. Methodological, v. 10, n. 2, p. 243-51. DOI: 10.1111/j.2517-6161.1948.tb00012.x. DOI: https://doi.org/10.1111/j.2517-6161.1948.tb00012.x
Olea, R.A. (2006) A six-step practical approach to semivariogram modeling. Stochastic Environmental Research and Risk Assessment, v. 20, n. 5, p. 307-18. DOI: 10.1007/s00477-005-0026-1. DOI: https://doi.org/10.1007/s00477-005-0026-1
Oliver, M.A. and R. Webster (2015) Basic Steps in Geostatistics: The Variogram and Kriging. Cham: Springer. DOI: 10.1007/978-3-319-15865-5. DOI: https://doi.org/10.1007/978-3-319-15865-5
Ortúzar, J. de D. and L.G. Willumsen (2011) Modelling Transport. Oxford: John Wiley & Sons. DOI: 10.1002/9781119993308. DOI: https://doi.org/10.1002/9781119993308
Paradis, E.; J. Claude and K. Strimmer (2004) APE: Analyses of Phylogenetics and Evolution in R language. Bioinformatics, v. 20, n. 2, p. 289-90. DOI: 10.1093/bioinformatics/btg412. PMid:14734327. DOI: https://doi.org/10.1093/bioinformatics/btg412
Pebesma, E.J. (2004) Multivariable geostatistics in S: the gstat package. Computers & Geosciences, v. 30, n. 7, p. 683-91. DOI: 10.1016/j.cageo.2004.03.012. DOI: https://doi.org/10.1016/j.cageo.2004.03.012
Pulugurtha, S.S. and P.R. Kusam (2012) Modeling annual average daily traffic with integrated spatial data from multiple network buffer bandwidths. Transportation Research Record: Journal of the Transportation Research Board, v. 2291, n. 1, p. 53-60. DOI: 10.3141/2291-07. DOI: https://doi.org/10.3141/2291-07
Pulugurtha, S.S. and S. Mathew (2021) Modeling AADT on local functionally classified roads using land use, road density, and nearest nonlocal road data. Journal of Transport Geography, v. 93, p. 103071. DOI: 10.1016/j.jtrangeo.2021.103071. DOI: https://doi.org/10.1016/j.jtrangeo.2021.103071
R Core Team (2021) R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Available at: <https://www.r-project.org/> (accessed 06/03/2023).
Remy, N.; A. Boucher and J. Wu (2009) Applied Geostatistics with Sgems: A User’s Guide. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9781139150019. DOI: https://doi.org/10.1017/CBO9781139150019
Ribeiro Jr, P.J. and P.J. Diggle (2016). geoR: Analysis of Geostatistical Data. R package version 1.7-5.2. Available at: <https://CRAN.R-project.org/package=geoR> (accessed 06/03/2023).
Sarlas, G. and K. W. Axhausen (2015) Prediction of AADT on a nationwide network based on an accessibility-weighted centrality measure. Arbeitsberichte Verkehrs- und Raumplanung, 1094, 1-21.
Selby, B. and K.M. Kockelman (2013) Spatial prediction of traffic levels in unmeasured locations: applications of universal kriging and geographically weighted regression. Journal of Transport Geography, v. 29, p. 24-32. DOI: 10.1016/j.jtrangeo.2012.12.009. DOI: https://doi.org/10.1016/j.jtrangeo.2012.12.009
Shamo, B.; E. Asa and J. Membah (2015) Linear spatial interpolation and analysis of annual average daily traffic data. Journal of Computing in Civil Engineering, v. 29, n. 1, p. 4014022. DOI: 10.1061/(ASCE)CP.1943-5487.0000281. DOI: https://doi.org/10.1061/(ASCE)CP.1943-5487.0000281
Sharma, S.; P. Lingras; F. Xu et al. (2001) Application of neural networks to estimate AADT on low-volume roads. Journal of Transportation Engineering, v. 127, n. 5, p. 426-32. DOI: 10.1061/(ASCE)0733-947X(2001)127:5(426). DOI: https://doi.org/10.1061/(ASCE)0733-947X(2001)127:5(426)
Song, I. and D. Kim (2022) Three common machine learning algorithms neither enhance prediction accuracy nor reduce spatial autocorrelation in residuals: an analysis of twenty-five socioeconomic data sets. Geographical Analysis, p. gean.12351. DOI: 10.1111/gean.12351. DOI: https://doi.org/10.1111/gean.12351
Song, Y.; X. Wang; G. Wright et al. (2019) Traffic volume prediction with segment-based regression kriging and its implementation in assessing the impact of heavy vehicles. IEEE Transactions on Intelligent Transportation Systems, v. 20, n. 1, p. 232-43. DOI: 10.1109/TITS.2018.2805817. DOI: https://doi.org/10.1109/TITS.2018.2805817
Souza, V.H.P. and M.R. Silveira (2009) Aspectos econômicos e infraestrutura rodoviária no estado de São Paulo: uma relação solidária. In: XII Encuentro de Geógrafos da América Latina - Caminando a una América Latina en Trasnformación (p. 1–16). Montevideo, Uruguay: Universidad de la República.
Stelzenmüller, V.; S. Ehrich and G.P. Zauke (2005) Impact of additional small-scale survey data on the geostatistical analyses of demersal fish species in the North Sea. Scientia Marina, v. 69, n. 4, p. 587-602. DOI: 10.3989/scimar.2005.69n4587. DOI: https://doi.org/10.3989/scimar.2005.69n4587
Tobler, W.R. (1970) A computer movie simulating urban growth in the detroit region. Economic Geography, v. 46, p. 234-40. DOI: 10.2307/143141. DOI: https://doi.org/10.2307/143141
UFRJ (2018) Nota Técnica Nº 003/2018/DE: Síntese do Desenvolvimento Técnico-Científico da Metodologia para Estimativa do Volume Médio Diário Anual - VMDa em Toda a Malha Rodoviária Federal Pavimentada. Rio de Janeiro: Universidade Federal do Rio de Janeiro.
Ver Hoef, J.M. (2018) Kriging models for linear networks and non-Euclidean distances: cautions and solutions. Methods in Ecology and Evolution, v. 9, n. 6, p. 1600-13. DOI: 10.1111/2041-210X.12979. DOI: https://doi.org/10.1111/2041-210X.12979
Wang, T.; A. Gan and P.Alluri(2013) Estimating annual average daily traffic for local roads for highway safety analysis. Transportation Research Record: Journal of the Transportation Research Board, v. 2398, n. 1, p. 60-6. DOI: 10.3141/2398-07. DOI: https://doi.org/10.3141/2398-07
Wang, X. and K. Kockelman (2009) Forecasting network data. Transportation Research Record: Journal of the Transportation Research Board, v. 2105, n. 1, p. 100-8. DOI: 10.3141/2105-13. DOI: https://doi.org/10.3141/2105-13
Wong, A.H. and T.J. Kwon (2021) Advances in regression kriging-based methods for estimating statewide winter weather collisions: an empirical investigation. Future Transportation, v. 1, n. 3, p. 570-89. DOI: 10.3390/futuretransp1030030. DOI: https://doi.org/10.3390/futuretransp1030030
Yang, H.; J. Yang; L.D. Han et al. (2018) A Kriging based spatiotemporal approach for traffic volume data imputation. PLoS One, v. 13, n. 4, e0195957. DOI: 10.1371/journal.pone.0195957. PMid:29664928. DOI: https://doi.org/10.1371/journal.pone.0195957
Zhang, D. and X.C. Wang (2014) Transit ridership estimation with network Kriging: a case study of Second Avenue Subway, NYC. Journal of Transport Geography, v. 41, p. 107-15. DOI: 10.1016/j.jtrangeo.2014.08.021. DOI: https://doi.org/10.1016/j.jtrangeo.2014.08.021
Zou, H.; Y. Yue; Q. Li et al. (2012) An improved distance metric for the interpolation of link-based traffic data using kriging: a case study of a large-scale urban road network. International Journal of Geographical Information Science, v. 26, n. 4, p. 667-89. DOI: 10.1080/13658816.2011.609488 DOI: https://doi.org/10.1080/13658816.2011.609488
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Samuel de França Marques, Renan Favero, Cira Souza Pitombo
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who submit papers for publication by TRANSPORTES agree to the following terms:
- Authors retain copyright and grant TRANSPORTES the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors may enter into separate, additional contractual arrangements for the non-exclusive distribution of this journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in TRANSPORTES.
- Authors are allowed and encouraged to post their work online (e.g., in institutional repositories or on their website) after publication of the article. Authors are encouraged to use links to TRANSPORTES (e.g., DOIs or direct links) when posting the article online, as TRANSPORTES is freely available to all readers.
- Authors have secured all necessary clearances and written permissions to published the work and grant copyright under the terms of this agreement. Furthermore, the authors assume full responsibility for any copyright infringements related to the article, exonerating ANPET and TRANSPORTES of any responsibility regarding copyright infringement.
- Authors assume full responsibility for the contents of the article submitted for review, including all necessary clearances for divulgation of data and results, exonerating ANPET and TRANSPORTES of any responsibility regarding to this aspect.