Ingeniería ISSN Impreso: 1409-2441 ISSN electrónico: 2215-2652

Bayesian Hierarchical Tobit Models: an application to travel distance analysis

Jonathan Aguero-Valverde



The objective of travel distance models is to better understand travel behavior so that policies can be implemented for reducing travel and with that the externalities of transport such as air pollution, congestion, and crashes. Hierarchical Bayesian models offer a flexible framework to analyze travel behavior by allowing the study of short term decisions of the activity and travel choices as well as long term decisions of residential and employment location. Since travel distance is censored at zero for a significant fraction of the observations, parameter estimates obtained by conventional regression methods are biased. Consistent parameter estimates can be obtained by using the Tobit model. The purpose of this paper is to demonstrate the application of fully Bayesian Tobit hierarchical models to the analysis of travel distance; this with the goal of accommodating the multilevel and censored nature of the data.

Results show that the hierarchical Tobit Model performs significantly better than the non-hierarchical model as measure by the Deviance and Deviance Information Criteria. Further, the highly significant variance at the individual and location levels, demonstrates the importance of using a multilevel approach.

The distance traveled increases with years of study and job qualification. In addition, all the members of the household travel less than the householder and women travel less than men. Industry sectors also show significant differences in travel time: workers in the secondary and tertiary sectors travel farther than workers in the primary sector. Land price is significantly correlated with distance traveled in both residence and employment locations. 

Palabras clave

Travel distance; Bayesian Tobit hierarchical models; residential location; employment location

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Voorhees AM, Bellomo SJ, Schofer JL, Cleveland DE. Factors in Work Trip Lengths. Highway Res Rec. 1966; 141: 24-46.

Gruen AC. Travel time and transportation policy. J Urban Econ. 1980; 8(2): 264-271.

Izraeli O, McCarthy TR. Variations in Travel Distance, Travel Time and Model Choice among SMSAs. Journal of Transport Economics and Policy. 1985; 19(2): 139-160.

Golob TF, Wissen LV. A joint household travel distance generation and car ownership model. Transp Res Part B Method. 1989; 23(6): 471-491

Gordon P, Kumar A, Richardson HW. Gender differences in metropolitan travel behavior. Reg Stud. 1989; 23(6): 499-510.

Brännäs K, Laitila T. Modelling and prediction of travel distance by car. Transportation planning and technology. 1991; 16(2): 129-143.

Johnston-Anumonwo I. The Influence of Household Type on Gender Differences in Work Trip Distance. Prof Geogr. 1992: 44(2): 161-169.

Rouwendal J, Rietveld P. Changes in commuting distances of Dutch households. Urban Stud. 1994; 31(9): 1545-1557.

Aronsson T, Brännäs K. Household work travel time. Reg Stud. 1996; 30(6): 541-548.

Fang HA. A discrete–continuous model of households’ vehicle choice and usage, with an application to the effects of residential density. Transp Res Part B Method. 2008; 42(9): 736-758.

Manaugh K, Miranda-Moreno LF, El-Geneidy AM. The effect of neighborhood characteristics, accessibility, home–work location, and demographics on commuting distances. Transportation.2010: 37(4): 627-646.

Ortuzar J, Willumsen LG. Modelling transport. 3rd ed. John Wiley & Sons; 2011.

Miller EJ. Land use transportation modeling. In: Goulias KG, editor. Transportation Systems Planning, Methods and Applications. Boca Raton: CRC Press; 2003.

McQuaid RW. A model of the travel to work limits of parents. Research in Transportation Economics. 2009; 25(1): 19-28.

Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis. 2nd ed. London: Chapman & Hall/CRC; 2003.

Salomon I. Ben-Akiva M. The use of the life-style concept in travel demand models. Environ Plan A. 1983; 15(5): 623-638.

Tobin J. Estimation of relationships for limited dependent variables. Econometrica. 1958: 26(1): 24-36.

Redmond LS, Mokhtarian PL. The positive utility of the commute: modeling ideal commute time and relative desired commute amount. Transportation. 2001; 28(2): 179-205.

Golob TF. The dynamics of household travel time expenditures and car ownership decisions. Transp Res Part A General. 1990; 24(6): 443-463.

Schwanen T, Mokhtarian PL. What if you live in the wrong neighborhood? The impact of residential neighborhood type dissonance on distance traveled. Transp Res D Transp Environ. 2005; 10(2): 127-151.

Greene WH. Econometric Analysis. 7th ed. Pearson; 2012.

Aguiar-Moya JP, Prozzi JA. Accounting for Censoring and Unobserved Heterogeneity in Pavement Cracking. Journal of Infrastructure Systems. 2014: 21(2): 04014044.

Congdon P. Bayesian statistical modelling. John Wiley & Sons; 2001.

Yang J, Miwa T, Morikawa T, Yamamoto T. Forecasting the Demand of Electric Vehicle Ownership and Usage in the Chukyo Region in Japan. Fourth International Conference on Transportation Engineering, American Society of Civil Engineers. 2013: 245-251

Brownstone D, Fang HA. A vehicle ownership and utilization choice model with endogenous residential density. J Transp Land Use. 2014; 7(2): 135-151

Spiegelhalter D, Best N, Carlin BP, Linde A. Bayesian Measures of Model Complexity and Fit. J R Stat Soc Series B Stat Methodol. 2002; 64(4): 583–639.

Lunn D, Spiegelhalter D, Thomas A, Best N. The BUGS project: Evolution, critique, and future directions, Stat Med. 2009; 28: 3049-3067.

Maat K. Timmermans H. A causal model relating urban form with daily travel distance through activity/travel decisions. Transportation Planning and Technology. 2009;32(2): 115-134

Wilson FD. Journey to Work: Metropolitan-nonmetropolitan comparisons. Institute for research on Poverty. University of Wisconsin-Madison, 1976.

Feng J, Dijst M, Wissink B, Prillwitz J. The impacts of household structure on the travel behavior of seniors and young parents in China. J Transp Geogr. 2013; 30: 117-126.

LaMondia J, Aultman-Hall L, Greene E. Long-Distance Work and Leisure Travel Frequencies: Ordered Probit Analysis Across Non-Distance-Based Definitions. Transp Res Rec. 2014; 2413: 1-12.

Jorritsma P, Schaap NTW. Families on the run: How do Dutch households with young children organize their travel behavior? In 5th International Conference on Women's Issues in Transportation. 2014: 97-108.

Vance C, Hedel R. The Impact of Urban Form on Automobile Travel: Disentangling Causation from Correlation. Transportation. 2007; 34: 575-588.

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