Vol. 14 No. 1 (2023):
Research Article

Comparing student mobility pattern models

Marie-Louise Litmeyer
Justus Liebig University
Philipp Gareis
Federal Institute for Research on Building, Urban Affairs and Spatial Development (BBSR), Germany
Stefan Hennemann
Department of Geography, Justus Liebig University Giessen, Gießen, Germany
Development of high school graduates per 100,000 inhabitants. Description: The high school graduates per 100,000 inhabitants for the years are presented. It is important for the interpretation that in 2011 in Bavaria and Lower Saxony and in 2016 in Schleswig-Holstein two cohorts took their A-Level exams.

Published 2023-03-17


  • Student Mobility,
  • Gravity Model,
  • Radial Model,
  • Germany,
  • Student mobility data

How to Cite

Litmeyer, Marie-Louise, Philipp Gareis, and Stefan Hennemann. 2023. “Comparing Student Mobility Pattern Models”. European Journal of Geography 14 (1):21-34. https://doi.org/10.48088/ejg.m.lit. .
Received 2023-01-20
Accepted 2023-03-17
Published 2023-03-17


Classically, gravity models have been used to estimate mobility flows. However, in recent years, a number of new models, such as radiation models, have been introduced to estimate human mobility. The focus has generally been on models dealing with commuting movements. There is no systematic application of different versions of the laws of gravity to student mobility. The application of these models to student mobility provides the opportunity to calculate reliable forecasts of student mobility flows at the micro level, make medium- to long-term decisions at the university level, and implement sustainable strategic orientation. Therefore, this article uses different models to estimate interactions to improve the forecast of the regional distribution of students in Germany under data limitations. Using publicly available data on high school graduates and historical data on student flows between German counties, we show that radiative models with parameters are best suited to predict student flows at the level of German counties. Among parameter-free models, the population-weighted odds model yields the best results.

- Forecasting student mobility flows in Germany
- Model comparison between gravity and radiation models
- Implications for the development of universities


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  1. Alm, J., & Winters, J. V. (2009). Distance and intrastate college student migration. Economics of Education Review, 28(6), 728–738. https://doi.org/10.1016/j.econedurev.2009.06.008
  2. Azad, M., Abdelqader, D., Taboada, L. M., & Christopher R. Cherry, C (2021): Walk-to-transit demand estimation methods applied at the parcel level to improve pedestrian infrastructure investment. Journal of Transport Geography 92. https://doi.org/10.1016/j.jtrangeo.2021.103019
  3. Balcan, D., Colizza, V., Goncalves, B., Hud, H., Ramasco, J., & Vespignani, A. (2009). Multiscale mobility networks and the spatial spreading of infectious diseases. Proceedings of the National Academy of Sciences, 106(51), 21484-21489. https://doi.org/10.1073/pnas.0906910106
  4. Bartzokas-Tsiompras, A. & Photis, Y. (2019): Measuring rapid transit accessibility and equity in migrant communities across 17 European cities. International Journal of Transport Development and Integration 3 (3), 245–258. https://doi.org/10.2495/TDI-V3-N3-245-258.
  5. Bergstrand, J. (1985). The gravity equation in international trade: some microeconomic foundations and empirical evidence. The Review of Economics and Statistics (67), 474–481. https://doi.org/10.2307/1925976
  6. Buenstorf, G., Geissler, M., & Krabel, S. (2016). Locations of labor market entry by German university graduates: is (regional) beauty in the eye of the beholder?. Review of Regional Research, 36(1), 29-49. https://doi.org/10.1007/s10037-015-0102-z
  7. Breznik, K., & Skrbinjek, V. (2020). Erasmus student mobility flows. European Journal of Education, 55(1), 105-117.Carey, H.C. (1858). Principles of Social Science. Lippincott.
  8. Champion, T. (2022). The United Kingdom’s ‘going away to university’migration and its changing impact on local populations in the twenty-first century. Local Economy, 37(4), 279-296.
  9. Choudaha, R. (2017). Three waves of international student mobility (1999–2020). Studies in Higher Education, 42(5), 825-832.
  10. Cooke, T. J., & Boyle, P. (2011). The migration of high school graduates to college. Educational Evaluation and Policy Analysis, 33(2), 202-213. https://doi.org/10.3102/0162373711399092
  11. Cullinan, J., & Duggan, J. (2016). A School-Level Gravity Model of Student Migration Flows to Higher Education Institutions. Spatial Economic Analysis, 11(3), 294-314. https://doi.org/10.1080/17421772.2016.1177195
  12. Deutscher Bundestag (2011). Aussetzung der allgemeinen Wehrpflicht beschlossen. Retrieved June 10, 2019, from https://www.bundestag.de/dokumente/textarchiv/2011/33831649_kw12_de_wehrdienst-204958
  13. Erlander, S., & Stewart, NF. (1990). The gravity model in transportation analysis: theory and extensions. Topics in transportation. VSP.
  14. Faggian, A., & Franklin, R. S. (2014). Human capital redistribution in the USA: the migration of the college-bound. Spatial Economic Analysis, 9 (4), 376–395. https://doi.org/10.1080/17421772.2014.961536
  15. Fagiolo, G. (2010). The international-trade network: gravity equations and topological properties. Journal of Economic Interaction and Coordi-nation 5, 1–25. https://doi.org/10.1007/s11403-010-0061-y
  16. FDZ (1992-2017). Froschungsdatenzentrum: Statistik der Studenten. Retrieved June 6, 2019, https://www.forschungsdaten-zentrum.de/de/bildung/studenten.
  17. Framhein, G. (1983). Alte und neue Universitäten. Einzugsbereiche und Ortswahl der Studenten, Motive und Verhalten. In Der Bundesminister für Bildung und Wissenschaft (Eds.), Schriftenreihe Hochschule, (44). Bock.
  18. Gareis, P. / Broekel, T. (2022): The Spatial Patterns of Student Mobility Before, During and After the Bologna Process in Germany. Tijdschrift voor economische en sociale geography. https://doi.org/10.1111/tesg.12507.
  19. Gösta, G., & von Stuckrad, T. (2007). Die Zukunft vor den Toren. Aktualisierte Berechnungen zur Entwicklung der Studienanfängerzahlen bis 2020. Retrieved November 13, 2020, from https://www.che.de/download/che_prognose_studienanfaengerzahlen_ap100-pdf/?wpdmdl=11190&ind=5d1a0a27b4528
  20. Griffith, D.A. (2009). Modeling spatial autocorrelation in spatial interaction data: empirical evidence from 2002 Germany journey-to-work flows. Journal of Geographical Systems, 11, 117–140. https://doi.org/10.1007/s10109-009-0082-z
  21. Haussen, T., & Uebelmesser, S. (2018). No place like home? Graduate migration in Germany. Growth and Change, 49(3), 442-472. https://doi.org/10.1111/grow.12249
  22. Hillman, N. W. (2016). Geography of college opportunity: The case of education deserts. American Educational Research Journal, 53(4), 987–1021. https://doi.org/10.3102/0002831216653204
  23. HMWK (2015). Hochschulpakt 2016 – 2020. Retrieved July 12, 2019, from https://wissenschaft.hessen.de/si-tes/default/files/media/hmwk/hsp_2016-2020.pdf
  24. Hong, I., & Jung, W.S. (2016). Application of gravity model on the Korean urban bus network. Physica A: Statistical Mechanics and its Applica-tions, 46, 48–55. https://doi.org/10.1016/j.physa.2016.06.055
  25. INKAR (2020): Indikatoren und Karten zur Raum- und Stadtentwicklung. Retrieved May 11, 2020, https://www.inkar.de
  26. Jung, W.S., Wang, F., & Stanley, H. (2008). Gravity model in the Korean highway. Europhysics Letters Association, 81(4). https://doi.org/10.1209/0295-5075/81/48005
  27. Kaluza, P., Kölzsch, A., Gastner, M.T., & Blasius, B. (2010). The complex network of global cargo ship movements. Journal of the Royal Society Interface, 7, 1097–1103. https://doi.org/10.1098/rsif.2009.0495
  28. Kang, C., Liu, Y., Guo, D., & Qin, K. (2015). A Generalized Radiation Model for Human Mobility: Spatial Scale, Searching Direction and Trip Con-straint. PLoS ONE ,10, Article e0143500. https://doi.org/10.1371/journal.pone.0143500.g003
  29. Kauder, B., & Potrafke, N. (2013). Government Ideology and Tuition Fee Policy: Evidence from the German States. CESifo Working Paper, No. 4205, Center for Economic Studies and ifo Institute (CESifo), Munich.
  30. Kluge, L. / Schewe, J. (2021): Evaluation and extension of the radiation model for internal migration. Phys. Rev. E 104, 054311. https://doi.org/10.1103/PhysRevE.104.054311
  31. KMK (2005). Prognose der Studienanfänger, Studierenden und Hochschulabsolventen bis 2020. Retrieved October 23, 2020, from https://www.kmk.org/fileadmin/veroeffentlichungen_beschluesse/2005/2005_10_01-Studienanfaenger-Absolventen-2020.pdf
  32. KMK (2011). Bestandsaufnahme und Perspektiven der Umsetzung des Bologna-Prozesses. Retrieved May 6, 2019, from https://www.kmk.org/fileadmin/veroeffentlichungen_beschlu-esse/2011/2011_03_10-Bestandsaufnahme-Bologna-Prozess.pdf
  33. KMK (2012). Vorausberechnung der Studienanfängerzahlen 2012-2025. Fortschreibung. Stand, 24, 2012. Retrieved April 1, 2019, from https://www.kmk.org/fileadmin/Dateien/pdf/Statistik/Vorausberechnung_der_Studienanfaengerzahlen_2012-2025_01.pdf
  34. Kramer, J.W. (2005). Zur Prognose der Studierendenzahlen in Mecklenburg-Vorpommern bis 2020, Wismarer Diskussionspapiere, No. 12/2005, HochschuleWismar, Fachbereich Wirtschaft, Wismar.
  35. Krings, G., Calabrese, F., Ratti, C., & Blondel, V.D. (2009). Urban gravity: a model for inter-city telecommunication flows. Journal of Statistical Mechanics Theory and Experiment, 2009(7). https://doi.org/10.1088/1742-5468/2009/07/L07003
  36. Lenormand, M., Huet, S., Gargiulo, F., & Deuant, G. (2012). A universal model of commuting networks. PLoS One, 7, Article, e45985. https://doi.org/10.1371/journal.pone.0045985
  37. Lenormand, M., Bassolas, A., & Ramasco, J. J. (2016). Systematic comparison of trip distributionlaws and models. Journal of Transport Geog-raphy, 51, 158-169. https://doi.org/10.1016/j.jtrangeo.2015.12.008
  38. Liang, X., Zhao, J., Dong, L., & Xu, K. (2013). Unraveling the origin of exponential law in intraurban human mobility. Scientific Reports, 3, Article 2983. https://doi.org/10.1038/srep02983
  39. Liu, Y, Sui, Z, Kang, C, & Gao, Y. (2014). Uncovering patterns of inter-urban trip and spatial interaction from social media check-in data. PLoS One, 9 Article e86026. https://doi.org/10.1371/journal.pone.0086026
  40. Liu, E., & Yan, X. (2019). New parameter-free mobility model: Opportunity priority selection model. Physica A, 526. https://doi.org/10.1016/j.physa.2019.04.259.
  41. Masucci, A., Serras, J., Johansson, A., & Batty, M. (2013). Gravity versus radiation models: on the importance of scale and heterogeneity in commuting fows. Physical Review, 88(2). https://doi.org/10.1103/PhysRevE.88.022812
  42. Maris, M., Jovacik, M., & Fazikova (2019). Commuting Trends and Patterns Behind the Regional Imbalances in Slovakia. European Journal of Geography 10 (1).
  43. Marshall, J.M., Wu, S.L., Sanchez C., Kiware, S.S., Ndhlovu, M., Ouédraogo, A.L., Touré, M.B., Sturrock, H. J., Ghani, A. C., & Ferguson, N. M. (2018). Mathematical models of human mobility of relevance to malaria transmission in Africa. Scientific Reports, 8, Article. https://doi.org/10.1038/s41598-018-26023-1
  44. McCune, Bruce & Grace, James (2002): Analysis of Ecological Communities. MjM Software Design. Gleneden Beach.
  45. Multrus F., Majer, S., Bargel, T., & Schmidt, M. (2017). Studiensituation und studentische Orientierungen. In Bundesministerium fuer Bildung und Forschung (BMBF). 13. Studierendensurvey an Universitäten und Fachhochschulen. Bonn, Berlin.
  46. Murat, C.H. (2010). Sample size needed for calibrating trip distribution and behavior of the gravity model. Journal of Transport Geography, 18(1), 183–190. https://doi.org/10.1016/j.jtrangeo.2009.05.013
  47. Nutz, M. (1991). Räumliche Mobilität der Studierenden und Struktur des Hochschulwesens in der Bundesrepublik Deutschland. Köln.
  48. Odlyzko, A. (2015). The forgotten discovery of gravity models and the inefficiency of early railway networks. OEconomia, 5, 157–192. https://doi.org/10.4000/oeconomia.1684
  49. Pan, R.K., Kaski, K., & Fortunato, S. (2012). World citation and collaboration networks: uncovering the role of geography in science. Scientific Reports,2, Article 902. https://doi.org/10.1038/srep00902
  50. Rees, P. (1986). A geographical forecast of the demand for student places. Transactions of the Institute of British Geographers, 5-26.
  51. Ren, Y., Ercsey-Ravasz, M., Wang, P., González, M. C., & Toroczkai, Z. (2014). Predicting commuter flows in spatial networks using a radiation model based on temporal ranges. Nature Communications, 5, Article 5347. https://doi.org/10.1038/ncomms6347
  52. Sá, C., Florax, R. J., & Rietveld, P. (2004). Determinants of the regional demand for higher education in the Netherlands: a gravity model ap-proach. Regional Studies, 38(4), 375-392. https://doi.org/10.1080/03434002000213905
  53. Sallah, K., Giorgi, R., Bengtsson, L., Lu, X., Wetter, E., Adrien, P., Rebaudet, S., Piarroux, R., & Gaudart, J. (2017). Mathematical models for pre-dicting human mobility in the context of infectious disease spread: introducing the impedance model. International Journal of Health Geographics, 16, Article 42. https://doi.org/10.1186/s12942-017-0115-7
  54. Simini, F., Gonzalez, M.C., Maritan, A., & Barabasi, A.L. (2012). A universal model for mobility and migration patterns. Nature, 484, 96-100. https://doi.org/10.1038/nature10856
  55. Soerensen T. (1948). A method of establishing groups of equal amplitude in plant sociology based on similarity of species and its application to analyses of the vegetation on danish commons. Biologiske Skriftler 5, 1-34.
  56. Statistisches Bundesamt (2008-2017). Fachserie 11 Reihe 4.1. Bildung und Kultur. Studierende an Hochschulen. Wintersemester 2007/2008 – Wintersemester 2016/2017. Wiesbaden.
  57. Tizzoni, M., Bajardi, P., Decuyper, A., Kon Kam King, G., Schneider, C.M., Blondel, V., Smoreda, Z., González, M., & Colizza, V. (2014). On the use of human mobility proxies for modeling epidemics. PLoS Computational Biology, 10, Article e1003716. https://doi.org/10.1371/journal.pcbi.1003716
  58. Thomas, T., & Tutert, S. (2013). An empirical model for trip distribution of commuters in the netherlands: transferability in time and space reconsidered. Journal of Transport Geography. 26, 158–165. https://doi.org/10.1016/j.jtrangeo.2012.09.005
  59. Tuite, A. R., Thomas-Bachli, A., Acosta, H., Bhatia, D., Huber, C. Petrasek, K., Watts, A., Yong, J.H.E., Bogoch, I. I., & Khan, K. (2018). Infectious disease implications of large-scale migration of Venezuelan nationals. Journal of Travel Medicine, 25(1). https://doi.org/10.1093/jtm/tay077
  60. Viboud, C., Bjørnstad, O.N., Smith, D.L., Simonsen, L., Miller, M.A., & Grenfell, B.T. (2006). Synchrony, waves, and spatial hierarchies in the spread of influenza. Science, 312(5772), 447–451.
  61. Weisser, R. (2019). How Personality Shapes Study Location Choices. Research in Higher Education,61, 88-116. https://doi.org/10.1007/s11162-019-09550-2
  62. Wilson, A., (1970). Entropy in urban and regional modelling. Pion, London.
  63. Wissenschaftliche Dienste des Deutschen Bundestages (2006). Der Studentenberg –Kollaps der Universitäten oder Illusion? Ein kritischer Bei-trag zur aktuellen Diskussion. Retrieved April 2, 2021, from https://www.bundestag.de/resource/blob/418880/251afebe1c84c24d81ad39c8bbf34334/WD-8-212-06-pdf-data.pdf
  64. Yan, X-Y., Zhao, C., Fan, Y., Di, Z., & Wang, W-X. (2014). Universal predictability of mobility patterns in cities. J. R. Soc. Interface, 11(100). http://doi.org/10.1098/rsif.2014.0834
  65. Yang, Y., Herrera, C., Eagle, N., & Gonzalez, M.C. (2014). Limits of predictability in commuting ows in the absence of data for calibration. Sci-entific Reports, 4, Article 5662. https://doi.org/10.1038/srep05662
  66. Zipf, G.K. (1946). The P1 P2/D hypothesis: on the intercity movement of persons. American Sociological Review, 11, 677–686.