Limited and Censored Dependent Variable Models

Reference work entry

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.

Keywords

Probit Model Spatial Effect Geographically Weight Regression Travel Mode Spatial Regression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Anselin L (2003) Spatial externalities, spatial multipliers, and spatial econometrics. Int Reg Sci Rev 26(2):153–166CrossRefGoogle Scholar
  2. 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):58–82CrossRefGoogle Scholar
  3. 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 169–196Google Scholar
  4. Bhat CR (2011) The maximum approximated composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models. Transp Res: Part B 45(7):923–939CrossRefGoogle Scholar
  5. 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):483–493CrossRefGoogle Scholar
  6. 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: J Transp Res Board 1921(1):70–78CrossRefGoogle Scholar
  7. 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
  8. 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: J Transp Res Board 2230(1):111–120CrossRefGoogle Scholar
  9. Fotheringham S (2003) Geographically weighted regression: the analysis of spatially varying relationships. Wiley, West SussexGoogle Scholar
  10. 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 172–188CrossRefGoogle Scholar
  11. Greene WH (2002) Econometric analysis, 5th edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
  12. Griffith DA (2000) Eigenfunction properties and approximations of selected incidence matrices employed in spatial analyses. Linear Algebra Appl 321(1–3):95–112CrossRefGoogle Scholar
  13. 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):460–471CrossRefGoogle Scholar
  14. LeSage JP (1999) Applied econometrics using MATLAB, http://www.spatial-econometrics.com/html/mbook.pdf. Accessed 1 Mar 2012
  15. LeSage JP, Pace RK (2009) Introduction to spatial econometrics. CRC Press/Taylor & Francis Group, Boca RatonCrossRefGoogle Scholar
  16. Luo J, Wei YHD (2009) Modeling spatial variations of urban growth patterns in Chinese cities: the case of Nanjing. Landscape Urban Plan 91(2):51–64CrossRefGoogle Scholar
  17. McFadden D (1980) Econometric models for probabilistic choice among products. J Bus 53(3):S13–S29CrossRefGoogle Scholar
  18. 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 189–228CrossRefGoogle Scholar
  19. McMillen DP, McDonald JF (1999) Land use before zoning: the case of 1920’s Chicago. Reg Sci Urban Econ 29(4):473–489CrossRefGoogle Scholar
  20. 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
  21. 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
  22. Pinkse J, Slade ME (1998) Contracting in space: an application of spatial statistics to discrete-choice models. J Econometrics 85(1):125–154CrossRefGoogle Scholar
  23. Sener I, Bhat C (2011) Flexible spatial dependence structures for unordered multinomial choice models: formulation and application to teenagers’ activity participation. Transportation 39(13):657–683Google Scholar
  24. 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 127–160CrossRefGoogle Scholar
  25. Train K (2003) Discrete choice methods with simulation. Cambridge University Press, New YorkCrossRefGoogle Scholar
  26. Varin C (2008) On composite marginal likelihoods. AStA Adv Stat Anal 92(1):1–28CrossRefGoogle Scholar
  27. Vijverberg WPM (1997) Monte Carlo evaluation of multivariate normal probabilities. J Econometrics 76(1–2):281–307CrossRefGoogle Scholar
  28. 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 173–194Google Scholar
  29. Wang X, Kockelman K (2009) Bayesian inference for ordered response data with a dynamic spatial-ordered probit model. J Reg Sci 49(5):877–913CrossRefGoogle Scholar
  30. 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 24:77–88CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringRensselaer Polytechnic InstituteTroyUSA

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