Abstract
The interest in bicycling and its determining factors is growing within the public health, transportation and geography communities. Ownership is one factor affecting bicycle usage, but work is still ongoing to not only quantify its effects but also to understand patterns in its growth and influence. In recent work, we mined and discovered patterns in global bicycle ownership that showed the existence of four characteristic country groups and their trends. Building on these results, we show in this paper that the ownership dataset can be modeled as a network. First, we observe mixing tendencies that indicate neighboring countries are more likely to be in the same ownership group and we map the likelihoods for cross-group mixings. Further, we define the strength of connections between countries by their proximity in ownership levels. We then determine the weighted degree assortative coefficient for the network and for each group relative to the network. We find that while the weighted degree assortativity of the ownership network is statistically insignificant, the highest and lowest ownership groups exhibit disassortative behavior with respect to the entire network. The second and third ranked groups, however, are strongly assortative. Our model serves as a step toward further work in studying the relationship between proximity and bicycle ownership among nations and unearthing possible patterns of influence. Considering further developments, this work can inform policy-relevant recommendations toward regional planning. This effort also contributes to expanding research in assortativity analyses, especially in weighted networks.
Similar content being viewed by others
Notes
The data and supporting code are available at www.ce.jhu.edu/sauleh/obls-gbu.
The error term is given by \(\varepsilon _{k} = \sqrt{\left(1 + \frac{1}{B}\right)\frac{1}{B} \sum _{b}\left\rbrace \log (W_{k,b}^{*}) - \frac{1}{B}\sum _{b}\log (W^{*}_{k,b})\right\lbrace ^{2}}\), where b is the index number of the generated sample (Tibshirani et al. 2001).
For a complete discussion on the global and group trends, please refer to Oke et al. (2015). Also, trends in bicycle ownership for each country in the dataset set can be viewed in Appendix B (Ibid).
Subsequent summations over i or j are over the same ranges indicated in Eq. 3.2.
Subsequent summations over b or c are on the same set D, except where otherwise noted.
References
Anagnostopoulos, A., Kumar, R., & Mahdian, M. (2008). Influence and correlation in social networks. In Proceedings of the 14th ACM SIGKDD international conference on knowledge discovery and data mining (KDD’08) (pp. 7–15). New York, NY, USA: ACM. doi:10.1145/1401890.1401897.
Baerveldt, C., Bunt, G., & Vermande, M. M. (2014). Selection patterns, gender and friendship aim in classroom networks. Zeitschrift für Erziehungswissenschaft, 17, 171–188. doi:10.1007/s11618-014-0546-x.
Barrat, A., Barthélemy, M., Pastor-Satorras, R., & Vespignani, A. (2004). The architecture of complex weighted networks. Proceedings of the National Academy of Sciences of the United States of America, 101(11), 3747–3752. doi:10.1073/pnas.0400087101.
Bellman, R., & Kalaba, R. (1959). A mathematical theory of adaptive control processes. Proceedings of the National Academy of Sciences of the United States of America, 4(2), 1–9.
Capocci, A., Servedio, V. D., Colaiori, F., Buriol, L. S., Donato, D., Leonardi, S., et al. (2006). Preferential attachment in the growth of social networks: The internet encyclopedia Wikipedia. Physical Review E, 74(3), 036,116.
Caprarelli, G., & Fletcher, S. (2014). A brief review of spatial analysis concepts and tools used for mapping, containment and risk modelling of infectious diseases and other illnesses. Parasitology, 141, 581–601.
Colquhoun, D. (2014). An investigation of the false discovery rate and the misinterpretation of p-values. Open Science, 1, 140216.
Dales, J., & Jones, P. (2014). International cycling infrastructure best practice study. London: Report for transport for London, Urban Movement, Phil Jones Associates.
Darmofal, D. (2015). Spatial analysis for the social sciences. Analytical methods for social research. New York, NY: Cambridge University Press.
Dijkstra, A., Hak, E., & Janssen, F. (2013). A systematic review of the application of spatial analysis in pharmacoepidemiologic research. Annals of Epidemiology, 23(8), 504–514.
Fleiss, J. L., Cohen, J., & Everitt, B. S. (1969). Large sample standard errors of kappa and weighted kappa. Psychological Bulletin, 72(5), 323–327.
Foster, J. G., Foster, D. V., Grassberger, P., & Paczuski, M. (2010). Edge direction and the structure of networks. Proceedings of the National Academy of Sciences, 107(24), 10,815–10,820. doi:10.1073/pnas.0912671107.
Giorgino, T. (2009). Computing and visualizing dynamic time warping alignments in R: The DTW package. Journal of Statistical Software, 31(7), 1–24.
Hens, N., Goeyvaerts, N., Aerts, M., Shkedy, Z., Van Damme, P., & Beutels, P. (2009). Mining social mixing patterns for infectious disease models based on a two-day population survey in Belgium. BMC Infectious Diseases, 9(1), 1–18. doi:10.1186/1471-2334-9-5.
Jacobsen, P. L. (2013). Safety in numbers: More walkers and bicyclists, safer walking and bicycling. Injury Prevention, 9(3), 205–209.
Jain, A. K., Murty, M. N., & Flynn, P. J. (1999). Data clustering: A review. ACM Computing Surveys, 31(3), 264–323.
Leung, C., & Chau, H. (2007). Weighted assortative and disassortative networks model. Physica A, 378(2), 591–602.
Li, H., Xu, S. H., & Kuo, W. (2014). Asymptotic analysis of simultaneous damages in spatial boolean models. Annals of Operations Research, 212(1), 139–154.
Ma, H., Fang, C., Pang, B., & Li, G. (2014). The effect of geographical proximity on scientific cooperation among Chinese cities from 1990 to 2010. PLoS ONE, 9(11), e111705. doi:10.1371/journal.pone.0111705.
Mérigot, B., Durbec, J. P., & Gaertner, J. C. (2010). On goodness-of-fit measure for dendrogram-based analyses. Ecology, 91(6), 1850–1859.
Midgley, P. (2011). Bicycle-sharing schemes: Enhancing sustainable mobility in urban areas. Background Paper 8, Global Transport Knowledge Partnership, International Road Federation, New York.
Milgram, S. (1967). The small-world problem. Psychology Today, 1(1), 61–67.
Newman, M. E. J. (2002). Assortative patterns in networks. Physical Review Letters, 89(20).
Newman, M. E. J. (2003). Mixing patterns in networks. Physical Review E, 67(2).
Newman, M. E. J. (2004). Detecting community structure in networks. The European Physical Journal B, 38, 321–330.
Noldus, R., & Van Mieghem, P. (2015). Assortativity in complex networks. Journal of Complex Networks, 3(4), 507–542. doi:10.1093/comnet/cnv005.
Oke, O., Bhalla, K., Love, D. C., & Siddiqui, S. (2015). Tracking global bicycle ownership patterns. Journal of Transport & Health, 2(4), 490–501.
Páez, A., & Scott, D. M. (2005). Spatial statistics for urban analysis: A review of techniques with examples. GeoJournal, 61(1), 53–67. doi:10.1007/s10708-005-0877-5.
Piraveenan, M., Prokopenko, M., & Zomaya, A. Y. (2010). Classifying complex networks using unbiased local assortativity. In Proceedings of the Alife XII conference (pp. 329–336). Odense, Denmark.
Piraveenan, M., Prokopenko, M., & Zomaya, A. (2012). Assortative mixing in directed biological networks. IEEE-ACM Transactions on Computational Biology and Bioinformatics, 9(1), 66–78.
Roseland, M. (2012). Toward sustainable communities: Solutions for citizens and their governments (4th ed.). Gabriola Island, BC: New Society Publishers.
Sakoe, H., & Chiba, S. (1978). Dynamic programming algorithm optimization for spoken word recognition. IEEE Transactions on ASSP, 26(1), 43–49.
Serrano, M. A., Boguná, M., Pastor-Satorras, R., & Vespignani, A. (2007). Large scale structure and dynamics of complex networks: From information technology to finance and natural sciences. World Scientific, chap Correlations in complex networks (pp. 35–66).
Small, H. (1973). Co-citation in the scientific literature: A new measure of the relationship between two documents. Journal of the American Society for Information Science, 24(4), 265–269.
Steglich, C., Snijders, T. A. B., & Pearson, M. (2010). Dynamic networks and behavior: Separating selection from influence. Sociological Methodology, 40(1), 329–393.
Szmyt, J. (2014). Spatial statistics in ecological analysis: From indices to functions. Silva Fennica. doi:10.14214/sf.1008.
Teichmann, S. A., & Babu, M. M. (2004). Gene regulatory network growth by duplication. Nature Genetics, 36(5), 492–496.
Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B, 63(2), 411–423.
Tsui, K. L., Chen, V. C. P., Jiang, W., & Aslandogan, Y. A. (2006). Springer handbook of engineering statistics, Book chapter data mining methods and applications (pp. 651–669). London: Springer.
Vandenbulcke-Plasschaert, G. (2011). Spatial analysis of bicycle use and accident risks for cyclists. Thèses de l’Université catholique de Louvain, Presses universitaires de Louvain, Louvain-la-Neuve, Belgium.
Vieira, I. T., Cheng, R. C. H., Harper, P. R., & de Senna, V. (2010). Small world network models of the dynamics of HIV infection. Annals of Operations Research, 178(1), 173–200.
Visualign. (2013). Number of neighbors for world countries. http://docs.google.com/spreadsheets/d/1agWAs620UntEQGY0yXUo5_C6zZesLEjBj1TVd3tTEDc/edit#gid=0. Accessed at http://visualign.wordpress.com/2011/10/06/number-of-neighbors-for-world-countries/.
Wall, R. S., Burger, M. J., & van der Knaap, G. A. B. (2011). The geography of global corporate networks: The poor, the rich, and the happy few countries. Environment and Planning A, 43, 904–927.
Zhukov, Y. M., & Stewart, B. M. (2013). Choosing your neighbors: Networks of diffusion in international relations. International Studies Quarterly, 57, 271–287.
Acknowledgements
We thank the participants of the 2014 INFORMS Workshop on Data Mining and Analytics participants for their valuable comments in the earlier stages of our work. The Gordon Croft Fellowship awarded by the Energy, Environment, Sustainability and Health Institute \((\hbox {E}^{2}\hbox {SHI})\) at The Johns Hopkins University, Baltimore, Maryland, funded this research in part. This quality of this paper was greatly improved as a result of the work of the two anonymous reviewers to whom the authors are grateful.
Author information
Authors and Affiliations
Corresponding author
Appendix: Country parameters
Appendix: Country parameters
Table 6 lists the degree parameters for each country. The code (written in Python) and supporting data for this work are available at http://modl.jhu.edu/resources/spatial-bicycle-ownership/.
Rights and permissions
About this article
Cite this article
Oke, O., Bhalla, K., Love, D.C. et al. Spatial associations in global household bicycle ownership. Ann Oper Res 263, 529–549 (2018). https://doi.org/10.1007/s10479-016-2358-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-016-2358-2