A brief discussion on the treatment of spatial correlation in multinomial discrete models
Francisco Bahamonde-Birke
DOI: https://doi.org/10.5198/jtlu.2021.1848
Keywords: multinomial discrete models, spatial correlation
Abstract
Spatial dependence plays a key role in all phenomena involving the geographic space, such as the social processes associated with transport and land use. Nevertheless, spatial dependence in multinomial discrete models has not received the same level of attention as have the other kinds of correlations in the discrete modeling literature, mainly due to the complexity of its treatment. This paper aims at offering a brief discussion on the different kinds of spatial correlation affecting multinomial discrete models and the different ways in which spatial correlation has been addressed in the discrete modeling literature. Furthermore, the paper offers a discussion on the advantages and limitations of the different approaches to treat spatial correlation and it also proposes a compromise solution among complexity, computational costs, and realism that can be useful in some specific situations.
References
Bhat, C. (2015). A new spatial (social) interaction discrete choice model accommodating for unobserved effects due to endogenous network formation. Transportation, 42(5), 879–914.
Bhat, C. R., & Guo, J. (2004). A mixed spatially correlated logit model: Formulation and application to residential choice modeling. Transportation Research Part B: Methodological, 38(2), 147–168.
Bierlaire, M. (2001). A general formulation of the cross-nested logit model. 1st Swiss Transport Research Conference, Ascona, Switzerland, March 1-3.
Bolduc, D., Fortin, B., & Fournier, M. A. (1996). The effect of incentive policies on the practice location of doctors: A multinomial probit analysis. Journal of Labor Economics, 14(4), 703–732.
Cardell, N. S., & Dunbar, F. C. (1980). Measuring the societal impacts of automobile downsizing. Transportation Research Part A: General, 14(5–6), 423–434.
Chakir, R., & Parent, O. (2009). Determinants of land-use changes: A spatial multinomial probit approach. Papers in Regional Science, 88(2), 327–344.
Chu, C. A. (1989). Paired combinatorial logit model for travel demand analysis. Proceedings of the Fifth World Conference on Transportation Research, 4, 295–309.
Cressie, N. (1993). Statistics for spatial data (Fourth ed.). Hoboken, NJ: John Wiley and Sons.
Czajkowski, M., Budziński, W., Campbell, D., Giergiczny, M., & Hanley, N. (2017). Spatial heterogeneity of willingness to pay for forest management. Environmental and Resource Economics, 68(3), 705–727.
Daly, A., & Bierlaire, M. (2003). A general and operational representation of GEV models (Technical report RO-030502). Lausanne, Switzerland: Institute of Mathematics, Operations Research Group ROSO, EPFL.
Daly, A. J., & Zachhary S. (1978). Improved multiple choice models. In D. A. Hensher, & M. Q Dalvi (Eds.), Determinants of travel choice (pp. 335–357). Westmead, UK: Saxon House.
Domencich, T., & McFadden, D. (1975). Urban travel demand–A behavioral analysis. Amsterdam: North-Holland Publishing.
Garrido, R. A., & Mahmassani, H. S. (2000). Forecasting freight transportation demand with the space–time multinomial probit model. Transportation Research Part B: Methodological, 34(5), 403–418.
LeSage, J. P. (2000). Bayesian estimation of limited dependent variable spatial autoregressive models. Geographical Analysis, 32(1), 19–35.
McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.), Frontiers in econometrics (pp. 105–142). New York: Academic Press.
McFadden, D. (1978). Modelling the choice of residential location. In A. Karlquist, L. Lundquist, F. Snickars, & J. Weibull. (Eds.) Spatial interaction theory and residential location (pp. 75–96). Amsterdam: North-Holland Publishing.
Ortúzar, J. de D., & Willumsen, L. G (2011). Modelling transport (Fourth ed.). Chichester, UK: John Wiley and Sons.
Parady, G. T., & Hato, E. (2016). Accounting for spatial correlation in tsunami evacuation destination choice: A case study of the Great East Japan Earthquake. Natural Hazards, 84(2), 797–807.
Schnier, K. E., & Felthoven, R. G. (2011). Accounting for spatial heterogeneity and autocorrelation in spatial discrete choice models: Implications for behavioral predictions. Land Economics, 87(3), 382–402.
Sener, I. N., Pendyala, R. M., & Bhat, C. R. (2011). Accommodating spatial correlation across choice alternatives in discrete choice models: An application to modeling residential location choice behavior. Journal of Transport Geography, 19(2), 294–303.
Sidharthan, R., & Bhat, C. R. (2012). Incorporating spatial dynamics and temporal dependency in land use change models. Geographical Analysis, 44(4), 321–349.
Thurstone, L. L. (1927). A law of comparative judgment. Psychological Review, 34, 273–286.
Tobler, W. R. (1970). A computer movie simulating urban growth in the Detroit region. Economic Geography, 46(1), 234–240.
Train, K. E. (2009). Discrete choice methods with simulation (Second ed.) Cambridge, UK: University Press.
Ward, M. D., & Gleditsch, K. S. (2002). Location, location, location: An MCMC approach to modeling the spatial context of war and peace. Political Analysis, 10(3), 244–260.
Wen, C. H., & Koppelman, F. S. (2001). The generalized nested logit model. Transportation Research Part B: Methodological, 35(7), 627–641.
Weiss, A., & Habib, K. N. (2017). Examining the difference between park and ride and kiss and ride station choices using a spatially weighted error correlation (SWEC) discrete choice model. Journal of Transport Geography, 59, 111–119.
Weiss, A., Hasnine, S., & Habib, K. N. (2019). A comparative study of alternative methods for capturing spatial correlations in discrete choice models through an empirical application on school choice location modelling. Paper presented at the 98th Annual Meeting of the Transportation Research Board, Washington, DC, January 13–17.
Williams, H. C. W. L. (1977). On the formation of travel demand models and economic evaluation measures of user benefit. Environment and Planning A, 9, 285–344.
Zhou, Y., Wang, X., & Holguín-Veras, J. (2016). Discrete choice with spatial correlation: A spatial autoregressive binary probit model with endogenous weight matrix (SARBP-EWM). Transportation Research Part B: Methodological, 94, 440–455.