Abstract
In regional science, many attributes, either social or natural, can be categorical. For example, choices of travel mode, presidential election outcomes, or quality of life can all be measured (and/or coded) as discrete responses, dependent on various influential factors. Some attributes, although continuous, are subject to truncation or censoring. For example, household income, when reported, tends to be censored, and only boundary values of a range are obtained. Such categorical and censored variables can be analyzed using econometric models that are established based on the concept of “unobserved/latent dependent variable.”
The previous examples also share another common feature: when data is collected in a spatial setting, they are all inevitably influenced by spatial effects, either spatial variation or spatial interaction. In contrast to panel data or time-series data, such variation or dependencies are two-dimensional, making it even more complicated. The need for investigating such limited and censored variables in a spatial context compels the quest for rigorous statistical methods.
This chapter introduces existing methods that are developed to analyze limited and censored dependent variables while considering the spatial effects. Different model specifications are discussed, with an emphasis on discrete response models and censored data models. Different types of spatial effects and corresponding ways to address them are then discussed. In general, when the spatial variation is of major concern, geographically weighted regression is preferred. When the spatial dependency is the primary interest, spatial filtering and spatial regression should be chosen. Techniques popularly used to estimate spatial limited variable models, including maximum simulated likelihood estimation, composite marginal likelihood estimation, and Bayesian approach, are also introduced and briefly compared.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Anselin L (2003) Spatial externalities, spatial multipliers, and spatial econometrics. Int Reg Sci Rev 26(2):153–166
Atkinson PM, German SE, Sear DA, Clark MJ (2003) Exploring the relations between riverbank erosion and geomorphological controls using geographically weighted logistic regression. Geogr Anal 35(1):58–82
Beron KJ, Vijverberg WPM (1999) Probit in a spatial context: a Monte Carlo analysis. In: Anselin L, Florax R, Rey S (eds) Advances in spatial econometrics, methodology, tools and applications. Springer, Berlin/Heidelberg/New York, pp 169–196
Bhat CR (2011) The maximum approximated composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models. Transp Res B 45(7):923–939
Dray S, Legendre P, Peres-Neto PR (2006) Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM). Ecol Model 196(3–4):483–493
Dugundji E, Walker J (2005) Discrete choice with social and spatial network interdependencies: an empirical example using mixed generalized extreme value models with field and panel effects. Transp Res Rec 1921(1):70–78
Ferdous N, Bhat CR (2012) Spatial panel ordered-response model with application to the analysis of urban land use development intensity patterns. Working paper. The University of Texas at Austin. http://amonline.trb.org/1smqfv/1smqfv/1. Accessed 1 Mar 2012
Ferdous N, Pendyala R, Bhat C, Konduri K (2011) Modeling the influence of family, social context, and spatial proximity on use of nonmotorized transport mode. Transp Res Rec 2230(1):111–120
Fotheringham S (2003) Geographically weighted regression: the analysis of spatially varying relationships. Wiley, West Sussex
Getis A (1995) Spatial filtering in a regression framework: experiments on regional inequality, government expenditures, and urban crime. In: New directions in spatial econometrics. Springer, Berlin/Heidelberg/New York, pp 172–188
Greene WH (2002) Econometric analysis, 5th edn. Prentice Hall, Upper Saddle River
Griffith DA (2000) Eigenfunction properties and approximations of selected incidence matrices employed in spatial analyses. Linear Algebra Appl 321(1–3):95–112
Klier T, McMillen DP (2008) Clustering of auto supplier plants in the U.S.: GMM spatial logit for large samples. J Bus Econ Stat 26(4):460–471
LeSage JP (1999) Applied econometrics using MATLAB. http://www.spatial-econometrics.com/html/mbook.pdf. Accessed 1 Mar 2012
LeSage JP, Pace RK (2009) Introduction to spatial econometrics. CRC Press/Taylor & Francis Group, Boca Raton
Luo J, Wei YHD (2009) Modeling spatial variations of urban growth patterns in Chinese cities: the case of Nan**g. Landsc Urban Plan 91(2):51–64
McFadden D (1980) Econometric models for probabilistic choice among products. J Bus 53(3):S13–S29
McMillen DP (1995) Spatial effects in probit models: a Monte Carlo investigation. In: Anselin L, Florax R (eds) New directions in spatial econometrics. Springer, Berlin/Heidelberg/New York, pp 189–228
McMillen DP, McDonald JF (1999) Land use before zoning: the case of 1920’s Chicago. Reg Sci Urban Econ 29(4):473–489
Pace RK, LeSage JP (2011) Fast simulated maximum likelihood estimation of the spatial probit model capable of handling large samples. http://ssrn.com/abstract=1966039. Accessed 15 Feb 2012
Paleti R, Bhat CR (2011) The composite marginal likelihood (CML) estimation of panel ordered-response models. Working paper. The University of Texas at Austin. http://www.caee.utexas.edu/prof/bhat/ABSTRACTS/CML_Paper_27July2010.pdf. Accessed 1 Jan 2012
Pinkse J, Slade ME (1998) Contracting in space: an application of spatial statistics to discrete-choice models. J Econ 85(1):125–154
Sener I, Bhat C (2011) Flexible spatial dependence structures for unordered multinomial choice models: formulation and application to teenagers’ activity participation. Transportation 39(13):657–683
Smith TE, LeSage JP (2004) A Bayesian probit model with spatial dependencies. In: Pace RK, LeSage JP (eds) Advances in econometrics: spatial and spatiotemporal econometric, vol 18. Elsevier, Oxford, pp 127–160
Train K (2003) Discrete choice methods with simulation. Cambridge University Press, New York
Varin C (2008) On composite marginal likelihoods. AStA Adv Stat Anal 92(1):1–28
Vijverberg WPM (1997) Monte Carlo evaluation of multivariate normal probabilities. J Econ 76(1–2):281–307
Wang X, Kockelman K (2008) Maximum simulated likelihood estimation with correlated observations: a comparison of simulation techniques. In: Sloboda B (ed) Transportation statistics. J. D. Ross Publishing, Fort Lauderdale, pp 173–194
Wang X, Kockelman K (2009) Bayesian inference for ordered response data with a dynamic spatial-ordered probit model. J Reg Sci 49(5):877–913
Wang X, Kockelman K, Lemp J (2012) The dynamic spatial multinomial probit model: analysis of land use change using parcel-level data. J Transp Geogr 24:77–88
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer-Verlag GmbH Germany, part of Springer Nature
About this entry
Cite this entry
Wang, X.(. (2021). Limited and Censored Dependent Variable Models. In: Fischer, M.M., Nijkamp, P. (eds) Handbook of Regional Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60723-7_92
Download citation
DOI: https://doi.org/10.1007/978-3-662-60723-7_92
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-60722-0
Online ISBN: 978-3-662-60723-7
eBook Packages: Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences