Model’s parameter sensitivity assessment and their impact on Urban Densification using regression analysis

Abstract

The impact of different global and local variables in urban development processes requires a systematic study to fully comprehend the underlying complexities in them. The interplay between such variables is crucial for modelling urban growth to closely reflects reality. Despite extensive research, ambiguity remains about how variations in these input variables influence urban densification. In this study, we conduct a global sensitivity analysis (SA) using a multinomial logistic regression (MNL) model to assess the model’s explanatory and predictive power. We examine the influence of global variables, including spatial resolution, neighborhood size, and density classes, under different input combinations at a provincial scale to understand their impact on densification. Additionally, we perform a stepwise regression to identify the significant explanatory variables that are important for understanding densification in the Brussels Metropolitan Area (BMA). Our results indicate that a finer spatial resolution of 50 m and 100 m, smaller neighborhood size of 5 × 5 and 3 × 3, and specific density classes—namely 3 (non-built-up, low and high built-up) and 4 (non-built-up, low, medium and high built-up)—optimally explain and predict urban densification. In line with the same, the stepwise regression reveals that models with a coarser resolution of 300 m lack significant variables, reflecting a lower explanatory power for densification. This approach aids in identifying optimal and significant global variables with higher explanatory power for understanding and predicting urban densification. Furthermore, these findings are reproducible in a global urban context, offering valuable insights for planners, modelers and geographers in managing future urban growth and minimizing modelling.

Keywords

Urban densification / Sensitivity analysis / Multinomial logistic regression / Stepwise regression

CRediT authorship contribution statement

Anasua Chakraborty: Writing – original draft, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Mitali Yeshwant Joshi: Writing – review & editing, Methodology, Investigation, Formal analysis, Conceptualization. Ahmed Mustafa: Writing – review & editing, Supervision, Conceptualization. Mario Cools: Supervision, Conceptualization. Jacques Teller: Writing – review & editing, Supervision, Investigation, Funding acquisition, Formal analysis.

Declaration of competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was funded by the INTER program and co-funded by the Fond National de la Recherche, Luxembourg (FNR) and the Fund for Scientific Research-FNRS, Belgium (F.R.S—FNRS), T.0233.20—‘Sustainable Residential Densification’ project (SusDens, 2020–2024).

References

[1] Abolhasani, S, Taleai, M, Karimi, M, Rezaee Node, A., 2016. Simulating urban growth under planning policies through parcel-based cellular automata (ParCA) model. Int. J. Geogr. Inf. Sci., 30 , pp. 2276-2301. doi: 10.1080/13658816.2016.1184271.

[2] Achmad, A, Hasyim, S, Dahlan, B, Aulia, D. N., 2015. Modeling of urban growth in tsunami-prone city using logistic regression: analysis of Banda Aceh, Indonesia. Appl. Geogr., 62 , pp. 237-246. doi: 10.1016/j.apgeog.2015.05.001.

[3] Giovanni, A., Simon, A., Andrew, R., 2020. Eurostat 2020. European Union, Luxembourg.

[4] Anputhas, M, Janmaat, J. J. A., Nichol, C. F., Wei, X., 2016. Modelling spatial association in pattern based land use simulation models. J. Environ. Manage., 181 , pp. 465-476. doi: 10.1016/j.jenvman.2016.06.034.

[5] Arlinghaus, S. L., Kerski, J. J., 2013. Spatial Mathematics: Theory and Practice through Mapping. CRC Press, Boca Raton . doi: 10.1201/B15049.

[6] Barredo, J. I., Kasanko, M, McCormick, N, Lavalle, C., 2003. Modelling dynamic spatial processes: simulation of urban future scenarios through cellular automata. Landsc. Urban Plan., 64 , pp. 145-160. doi: 10.1016/S0169-2046(02)00218-9.

[7] Bennett, R., Wallace, J., Williamson, I., 2008. Organising land information for sustainable land administration. Land Use Policy 25, 126–138. doi: 10.1016/J.LANDUSEPOL.2007.03.006.

[8] Boussauw, K., Allaert, G., Witlox, F., 2013. Colouring inside what lines? Interference of the urban growth boundary and the political–administrative border of Brussels. Eur. Plan. Stud. 21, 1509–1527. doi: 10.1080/09654313.2012.722952.

[9] Boussauw, K, Boelens, L., 2015. Fuzzy tales for hard blueprints: the selective coproduction of the Spatial Policy Plan for Flanders, Belgium. Environ. Plann. C Gov. Policy, 33 , pp. 1376-1393. doi: 10.1068/c12327.

[10] Calka, B, Nowak Da Costa, J, Bielecka, E., 2017. 8 , pp. 1440-1455. doi: 10.1080/19475705.2017.1345792.

[11] Cao, Y, Zhang, X, Fu, Y, Lu, Z, Shen, X., 2020. Urban spatial growth modeling using logistic regression and cellular automata: a case study of Hangzhou. Ecol. Indic., 113 , Article 106200. doi: 10.1016/J.ECOLIND.2020.106200.

[12] Chakraborty, A, Mustafa, A, Omrani, H, Teller, J. 2023. A framework to probe uncertainties in urban cellular automata modelling using a novel framework of multilevel density approach: a case study for Wallonia Region. R. Goodspeed, R. Sengupta, M. Kyttä, C. Pettit (Eds.), Intelligence for Future Cities: Planning Through Big Data and Urban Analytics (The Urban Book Series), Springer, Belgium, pp.325-341.

[13] Chakraborty, A., Omrani, H., Teller, J., 2022a. A comparative analysis of drivers impacting urban densification for cross regional scenarios in Brussels Metropolitan Area. Land 11, 2291. doi: 10.3390/LAND11122291.

[14] Chakraborty, A., Omrani, H., Teller, J., 2022b. Modelling the drivers of urban densification to evaluate built-up areas extension: a data-modelling solution towards zero net land take. In: Gervasi, O., Murgante, B., Hendrix, E.M.T., Taniar, D., Apduhan, B.O. (Eds.), Computational Science and Its Applications – ICCSA 2022 Workshop. Lecture Notes in Computer Science, 13376. Springer, Cham doi: 10.1007/978-3-031-10450-3_21.

[15] Chen, Y, Li, X, Liu, X, Ai, B., 2014. Modeling urban land-use dynamics in a fast developing city using the modified logistic cellular automaton with a patch-based simulation strategy. Int. J. Geogr. Inf. Sci., 28 , pp. 234-255. doi: 10.1080/13658816.2013.831868.

[16] Cheng, J, Masser, I., 2003. Urban growth pattern modeling: a case study of Wuhan city, PR China. Landsc. Urban Plan., 62 , pp. 199-217. doi: 10.1016/S0169-2046(02)00150-0.

[17] Claassens, J., Koomen, E., Rouwendal, J., 2020. Urban density and spatial planning: the unforeseen impacts of Dutch devolution. PLoS One 15, e0240738. doi: 10.1371/JOURNAL. PONE.0240738.

[18] Cortés-Borda, D, J-Polanco, A, Escobar-Sierra, M., 2022. Social perception assessment of hydropower sustainability: a stepwise logistic regression modeling. Environ. Sci. Policy, 134 , pp. 108-118. doi: 10.1016/J.ENVSCI.2022.03.026.

[19] Crooks, A., Castle, C., Batty, M., 2008. Key challenges in agent-based modelling for geo-spatial simulation. Comput. Environ. Urban Syst. 32, 417–430. doi: 10.1016/j.compenvurbsys.2008.09.004.

[20] Cuellar, Y, Perez, L., 2023. Assessing the accuracy of sensitivity analysis: an application for a cellular automata model of Bogota’s urban wetland changes. Geocarto Int., 38 (1) , Article 2186491. doi: 10.1080/10106049.2023.2186491.

[21] De Maesschalck, F, De Rijck, T, Heylen, V, Bruel, P., 2015. Crossing borders: social-spatial relations between Brussels and Flemish Brabant. Bruss. Stud. . doi: 10.4000/BRUSSELS.1260.

[22] Deboosere, P, Eggerickx, T, Van Hecke, E, Wayens, B., 2009. The population of Brussels: a demographic overview. Bruss. Stud. . doi: 10.4000/BRUSSELS.891.

[23] Dong, F, Li, J, Wang, Y, Zhang, X, Zhang, S, Zhang, S., 2019. Drivers of the decoupling indicator between the economic growth and energy-related CO₂ in China: a revisit from the perspectives of decomposition and spatiotemporal heterogeneity. Sci. Total Environ., 685 , pp. 631-658. doi: 10.1016/J.SCITOTENV.2019.05.269.

[24] Fawcett, T., 2006. An introduction to ROC analysis. Pattern Recognit. Lett., 27 , pp. 861-874. doi: 10.1016/J.PATREC.2005.10.010.

[25] Feng, Y, Liu, Y, Tong, X, Liu, M, Deng, S., 2011. Modeling dynamic urban growth using cellular automata and particle swarm optimization rules. Landsc. Urban Plan., 102 , pp. 188-196. doi: 10.1016/J.LANDURBPLAN.2011.04.004.

[26] Franczyk, A., 2019. Using the Morris sensitivity analysis method to assess the importance of input variables on time-reversal imaging of seismic sources. Acta Geophys., 67 , pp. 1525-1533. doi: 10.1007/S11600-019-00356-5.

[27] Gamboa, F, Gremaud, P, Klein, T, Lagnoux, A., 2022. Global sensitivity analysis: a novel generation of mighty estimators based on rank statistics. Bernoulli, 28 , pp. 2345-2374. doi: 10.3150/21-BEJ1421.

[28] Getu, K, Gangadhara Bhat, H., 2024. Application of geospatial techniques and binary logistic regression model for analyzing driving factors of urban growth in Bahir Dar city, Ethiopia. Heliyon, 10 , p. e25137. doi: 10.1016/J.HELIYON.2024.E25137.

[29] Guyot, M, Araldi, A, Fusco, G, Thomas, I., 2021. The urban form of Brussels from the street perspective: the role of vegetation in the definition of the urban fabric. Landsc. Urban Plan., 205 , Article 103947. doi: 10.1016/J.LANDURBPLAN.2020.103947.

[30] Halleux, J-M, Marcinczak, S, van der Krabben, E., 2012. The adaptive efficiency of land use planning measured by the control of urban sprawl. The cases of the Netherlands, Belgium and Poland. Land Use Policy, 29 , pp. 887-898. doi: 10.1016/j.landusepol.2012.01.008.

[31] Hao, P, Hooimeijer, P, Sliuzas, R, Geertman, S., 2013. What drives the spatial development of urban villages in China?. Urban Stud., 50 , pp. 3394-3411. doi: 10.1177/0042098013484534.

[32] Harris, P, Charlton, M, Fotheringham, A. S., 2010. Moving window kriging with geographically weighted variograms. Stoch. Environ. Res. Risk Assess., 24 , pp. 1193-1209. doi: 10.1007/S00477-010-0391-2.

[33] Hu, Z, Lo, C. P., 2007. Modeling urban growth in Atlanta using logistic regression. Comput. Environ. Urban Syst., 31 , pp. 667-688. doi: 10.1016/J.COMPENVURBSYS.2006.11.001.

[34] James, G, Witten, D, Hastie, T, Tibshirani, R., 2021. An Introduction to Statistical Learning: With Applications in R, 2nd Ed. Springer, New York, NY

[35] Kantakumar, L. N., Kumar, S, Schneider, K., 2020. What drives urban growth in Pune? A logistic regression and relative importance analysis perspective. Sust. Cities Soc., 60 , Article 102269. doi: 10.1016/J.SCS.2020.102269.

[36] Karimi, F, Sultana, S, Babakan, A. S., Suthaharan, S., 2021. Urban expansion modeling using an enhanced decision tree algorithm. Geoinformatica, 25 , pp. 715-731. doi: 10.1007/s10707-019-00377-8.

[37] Kocabas, V, Dragicevic, S., 2006. Assessing cellular automata model behaviour using a sensitivity analysis approach. Comput. Environ. Urban Syst., 30 , pp. 921-953. doi: 10.1016/J.COMPENVURBSYS.2006.01.001.

[38] Krongkaew, M., 2004. The development of the Greater Mekong Subregion (GMS): real promise or false hope?. J. Asian Econ., 15 , pp. 977-998. doi: 10.1016/J.ASIECO.2004.09.006.

[39] Li, X., Zhou, W., Ouyang, Z., 2013. Forty years of urban expansion in Beijing: what is the relative importance of physical, socioeconomic, and neighborhood factors? Appl. Geogr. 38, 1–10. doi: 10.1016/J.APGEOG.2012.11.004.

[40] Liu, B, Zhao, Q, Jin, Y, Shen, J, Li, C., 2021. Application of combined model of stepwise regression analysis and artificial neural network in data calibration of miniature air quality detector. Sci. Rep., 11 , p. 3247. doi: 10.1038/s41598-021-82871-4.

[41] Liu, X, Li, X, Shi, X, Wu, S, Liu, T., 2008. Simulating complex urban development using kernel-based non-linear cellular automata. Ecol. Modell., 211 , pp. 169-181. doi: 10.1016/J.ECOLMODEL.2007.08.024.

[42] Lu, B, Charlton, M, Harris, P, Fotheringham, A. S., 2014. Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data. Int. J. Geogr. Inf. Sci., 28 , pp. 660-681. doi: 10.1080/13658816.2013.865739.

[43] Moos, M, Mendez, P., 2015. Suburban ways of living and the geography of income: how homeownership, single-family dwellings and automobile use define the metropolitan social space. Urban Stud., 52 , pp. 1864-1882. doi: 10.1177/0042098014538679.

[44] Mustafa, A., Saadi, I., Cools, M., Teller, J., 2018a. Understanding urban development types and drivers in Wallonia: a multi-density approach. Int. J. Bus. Intell. Data Min. 13, 309–330. doi: 10.1504/IJBIDM.2018.088434.

[45] Mustafa, A., Van Rompaey, A., Cools, M., Saadi, I., Teller, J., 2018b. Addressing the determinants of built-up expansion and densification processes at the regional scale. Urban Stud. 55 (15), 3279–3298. doi: 10.1177/0042098017749176.

[46] Mustafa, A., Heppenstall, A., Omrani, H., Saadi, I., Cools, M., Teller, J., 2018c. Modelling built-up expansion and densification with multinomial logistic regression, cellular automata and genetic algorithm. Comput. Environ. Urban Syst. 67, 147–156. doi: 10.1016/J.COMPENVURBSYS.2017.09.009.

[47] Overmars, K. P., De Koning, G. H. J., Veldkamp, A., 2003. Spatial autocorrelation in multi-scale land use models. Ecol. Modell., 164 , pp. 257-270. doi: 10.1016/S0304-3800(03)00070-X.

[48] Pijanowski, B. C., Alexandridis, K. T., Müller, D., 2006. Modelling urbanization patterns in two diverse regions of the world. J. Land Use Sci., 1 , pp. 83-108. doi: 10.1080/17474230601058310.

[49] Poelmans, L, Van Rompaey, A., 2009. Detecting and modelling spatial patterns of urban sprawl in highly fragmented areas: a case study in the Flanders–Brussels region. Landsc. Urban Plan., 93 , pp. 10-19. doi: 10.1016/J.LANDURBPLAN.2009.05.018.

[50] Poelmans, L, Van Rompaey, A., 2010. Complexity and performance of urban expansion models. Comput. Environ. Urban Syst., 34 , pp. 17-27. doi: 10.1016/J.COMPENVURBSYS.2009.06.001.

[51] Pontius, R. G., Huffaker, D, Denman, K., 2004. Useful techniques of validation for spatially explicit land-change models. Ecol. Modell., 179 , pp. 445-461. doi: 10.1016/J.ECOLMODEL.2004.05.010.

[52] Puente-Sotomayor, F., Mustafa, A., Teller, J., 2021. Landslide susceptibility mapping of urban areas: logistic regression and sensitivity analysis applied to Quito, Ecuador. Geoenviron. Disasters 8, 19. doi: 10.1186/S40677-021-00184-0.

[53] Razavi, S, Jakeman, A, Saltelli, A, Prieur, C, Iooss, B, Borgonovo, E, Plischke, E, Lo Piano, S, Iwanaga, T, Becker, W, Tarantola, S, Guillaume, J. H. A., Jakeman, J, Gupta, H, Melillo, N, Rabitti, G, Chabridon, V, Duan, Q, Sun, X, Smith, S, Sheikholeslami, R, Hosseini, N, Asadzadeh, M, Puy, A, Kucherenko, S, Maier, H. R., 2021. The future of sensitivity analysis: an essential discipline for systems modeling and policy support. Environ. Modell. Softw., 137 , Article 104954. doi: 10.1016/J.ENVSOFT.2020.104954.

[54] Roodposhti, M. S., Hewitt, R. J., Bryan, B. A., 2020. Towards automatic calibration of neighbourhood influence in cellular automata land-use models. Comput. Environ. Urban Syst., 79 , Article 101416. doi: 10.1016/J.COMPENVURBSYS.2019.101416.

[55] Saganeiti, L, Mustafa, A, Teller, J, Murgante, B., 2021. Modeling urban sprinkling with cellular automata. Sust. Cities Soc., 65 , Article 102586. doi: 10.1016/J.SCS.2020.102586.

[56] Saltelli, A, Aleksankina, K, Becker, W, Fennell, P, Ferretti, F, Holst, N, Li, S, Wu, Q., 2019. Why so many published sensitivity analyses are false: a systematic review of sensitivity analysis practices. Environ. Modell. Softw., 114 , pp. 29-39. doi: 10.1016/J.ENVSOFT.2019.01.012.

[57] Seto, K. C., Güneralp, B, Hutyra, L. R., 2012. Global forecasts of urban expansion to 2030 and direct impacts on biodiversity and carbon pools. Proc. Natl. Acad. Sci. U.S.A., 109 , pp. 16083-16088. doi: 10.1073/PNAS.1211658109.

[58] Shafizadeh-Moghadam, H, Asghari, A, Taleai, M, Helbich, M, Tayyebi, A., 2017. Sensitivity analysis and accuracy assessment of the land transformation model using cellular automata. GISci. Remote Sens., 54 , pp. 639-656. doi: 10.1080/15481603.2017.1309125.

[59] Shu, B, Zhu, S, Qu, Y, Zhang, H, Li, X, Carsjens, G. J., 2020. Modelling multi-regional urban growth with multilevel logistic cellular automata. Comput. Environ. Urban Syst., 80 , Article 101457. doi: 10.1016/J.COMPENVURBSYS.2019.101457.

[60] Sun, L, Chen, J, Li, Q, Huang, D., 2020. Dramatic uneven urbanization of large cities throughout the world in recent decades. Nat. Commun., 11 , p. 5366. doi: 10.1038/s41467-020-19158-1.

[61] Todes, A., 2012. Urban growth and strategic spatial planning in Johannesburg, South Africa. Cities, 29 , pp. 158-165. doi: 10.1016/J.CITIES.2011.08.004.

[62] Vermeiren, K, Van Rompaey, A, Loopmans, M, Serwajja, E, Mukwaya, P., 2012. Urban growth of Kampala, Uganda: pattern analysis and scenario development. Landsc. Urban Plan., 106 , pp. 199-206. doi: 10.1016/J.LANDURBPLAN.2012.03.006.

[63] Waddell, P., 2002. UrbanSim: modeling urban development for land use, transportation, and environmental planning. J. Am. Plan. Assoc., 68 , pp. 297-314. doi: 10.1080/01944360208976274.

[64] Wang, M, Wright, J, Brownlee, A, Buswell, R., 2016. A comparison of approaches to stepwise regression on variables sensitivities in building simulation and analysis. Energy Build., 127 , pp. 313-326. doi: 10.1016/J.ENBUILD.2016.05.065.

[65] Wang, R., Feng, Y., Tong, X., Zhao, J., Zhai, S., 2021a. Impacts of spatial scale on the delineation of spatiotemporal urban expansion. Ecol. Indic. 129, 107896. doi: 10.1016/J.ECOLIND.2021.107896.

[66] Wang, H., Guo, J., Zhang, B., Zeng, H., 2021b. Simulating urban land growth by incorporating historical information into a cellular automata model. Landsc. Urban Plan. 214, 104168. doi: 10.1016/J.LANDURBPLAN.2021.104168.

[67] Wang, Y, Lv, W, Wang, M, Chen, X, Li, Y., 2023. Application of improved Moran's I in the evaluation of urban spatial development. Spat. Stat., 54 , Article 100736. doi: 10.1016/J.SPASTA.2023.100736.

[68] UN-HABITAT, 2020. World Cities Report 2020: The Value of Sustainable Urbanization. UN-HABITAT, Nairobi, Kenya.

[69] Wu, F., 2002. Calibration of stochastic cellular automata: the application to rural-urban land conversions. Int. J. Geogr. Inf. Sci., 16 , pp. 795-818. doi: 10.1080/13658810210157769.

[70] Wu, H, Lin, A, Xing, X, Song, D, Li, Y., 2021. Identifying core driving factors of urban land use change from global land cover products and POI data using the random forest method. Int. J. Appl. Earth Obs. Geoinf., 103 , p. 102475. doi: 10.1016/j.jag.2021.102475.

[71] Yang, W, Zou, X, Wang, M, Liu, P., 2023. A multinomial logistic regression model-based seismic risk assessment method for museum exhibition halls. J. Build. Eng., 69 , Article 106312. doi: 10.1016/J.JOBE.2023.106312.

[72] Zevenbergen, J., 2002. A Systems Approach to Land Registration and Cadastre. International Federation of Surveyors (FIG) XXII International Congress, Washington, D.C. USA