# Measurement of Opportunity Cost of Travel Time for Predicting Future Residential Mobility Based on the Smart Card Data of Public Transportation

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## Abstract

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## 1. Introduction

- We propose a method to infer the opportunity cost of travel time on non-working days that varies according to the departure place by extending the conventional travel cost method.
- We examine the extent to which the opportunity cost of travel time contributes to the prediction of future residential movements.

- RQ1: Does the opportunity cost of travel time calculated by an extended travel cost method contribute to the prediction of the number of people who relocate to each place compared to the current population and other indices?
- RQ2: Does the opportunity cost of travel time have a causal influence on the number of people who relocate to each place compared to the current population and other indices?

## 2. Related Works

#### 2.1. Travel Cost Method and Opportunity Cost of Travel Time

#### 2.2. Interaction between Urban Form and Travel Behavior

#### 2.3. Influential Factors on Residential Mobility

#### 2.4. Gap in the Literature

## 3. Method

#### 3.1. Measurement of Opportunity Cost of Travel Time

#### 3.2. Decision of the Prediction Model

## 4. Baselines and Evaluation Methods

#### 4.1. Baselines

- Population (P): This index is simply the number of current residents in place i. We let ${P}_{i,k}$ denote the number of residents of demographic group k living in place i.
- Average travel time (A): This index is a simplification of the opportunity cost of travel time. We let ${T}_{i,k}$ denote the multiplicative inverse of travel time per person.
- Entropy (E): According to Smith et al. [38], the diversity of places people visit reflects the well-being of the community. The index is as follows:$$diversity\left(u\right)=\frac{-{\sum}_{j\in {S}_{u}}{w}_{u,j}log\left({w}_{u,j}\right)}{|{S}_{u}|}$$$${H}_{i}=\frac{1}{|{M}_{i}|}\sum _{u\in {M}_{i}}diversity\left(u\right)$$In Equation (6), ${S}_{u}$ is the set of places user u visited, and ${w}_{u,j}$ is the proportion of all u’s visits to place j. The numerator in this equation is the Shannon entropy. In Equation (7), ${M}_{i}$ is the set of users who live in place i. We let ${H}_{i,k}$ denote the entropy of places users in demographic group k living in place i visit.

#### 4.2. Evaluation of the Correlation and Causal Relation between the Number of Relocations and the Predictors

## 5. Data

## 6. Data Pre-Processing

#### 6.1. Decision of Travel Time between Two Stations

#### 6.2. Grouping Departure Stations, Arrival Stations and Smart Card Holders

#### 6.3. Removing Records of Arrival Stations that Each User Frequently Visits

## 7. Results

#### 7.1. Results of the Regression of the Predictors to the Number of Residential Moves

#### 7.2. Causal Influences on the Number of Residential Moves

## 8. Discussion

## 9. Conclusions

- We have extended the conventional travel cost method to estimate the opportunity cost of travel time as a function of the departure place.
- We have confirmed that both the current population and the opportunity cost of travel time contribute to the prediction of the number of relocations.
- We have confirmed that most of the causal influence from the current population to residential mobility is mediated indirectly through the opportunity cost of travel time. Therefore, the opportunity cost of travel time is more effective at estimating changes in residential mobility caused by urban development.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

A | average travel time |

E | entropy |

ICTs | information and communication technologies |

LiNGAM | linear non-Gaussian acyclic model |

O | opportunity cost of travel time |

P | current population |

PMT | person miles traveled |

TCM | travel cost method |

TCM4MP | travel cost method for multiple places |

VMT | vehicle miles traveled |

## References

- Cervero, R.; Kockelman, K. Travel demand and the 3Ds: Density, diversity, and design. Trans. Res. Part D Trans. Environ.
**1997**, 2, 199–219. [Google Scholar] [CrossRef] - Rajamani, J.; Bhat, C.; Handy, S.; Knaap, G.; Song, Y. Assessing impact of urban form measures on nonwork trip mode choice after controlling for demographic and level-of-service effects. Trans. Res. Rec. J. Trans. Res. Board
**2003**, 158–165. [Google Scholar] [CrossRef] - Zhang, M. Exploring the relationship between urban form and nonwork travel through time use analysis. Landsc. Urban Plan.
**2005**, 73, 244–261. [Google Scholar] [CrossRef] - Ewing, R.; Cervero, R. Travel and the Built Environment. J. Am. Plan. Assoc.
**2010**, 76, 265–294. [Google Scholar] [CrossRef] - Quigley, J.M.; Weinberg, D.H. Intra- Urban Residential Mobility: A Review and Synthesis. Int. Reg. Sci. Rev.
**1977**, 2, 41–66. [Google Scholar] [CrossRef][Green Version] - Dieleman, F.M. Modelling residential mobility; a review of recent trends in research. J. Hous. Buil. Environ.
**2001**, 16, 249–265. [Google Scholar] [CrossRef] - Trice, A.H.; Wood, S.E. Measurement of recreation benefits. Land Econ.
**1958**, 34, 195–207. [Google Scholar] [CrossRef] - McConnell, K.E. Chapter 15 The economics of outdoor recreation. In Handbook of Natural Resource and Energy Economics; Elsevier: Amsterdam, The Netherlands, 1985; Volume 2, pp. 677–722. [Google Scholar]
- Walsh, R.G.; Sanders, L.D.; Mckean, J.R. The Consumptive Value Of Travel Time On Recreation Trips. J. Travel Res.
**1990**, 29, 17–24. [Google Scholar] [CrossRef] - Bockstael, N.E.; Strand, I.E.; Hanemann, W.M. Time and the Recreational Demand Model. Am. J. Agric. Econ.
**1987**, 69, 293–302. [Google Scholar] [CrossRef] - Jones, P.M. New Approaches to Understanding Travel Behavior: The Human Activity Approach; Oxford University: Oxford, UK, 1977. [Google Scholar]
- Becker, G.S. A Theory of the Allocation of Time. Econ. J.
**1965**, 75, 493–517. [Google Scholar] [CrossRef] - Lyons, G.; Urry, J. Travel time use in the information age. Trans. Res. Part A Policy Pract.
**2005**, 39, 257–276. [Google Scholar] [CrossRef][Green Version] - Lyons, G.; Jain, J.; Holley, D. The use of travel time by rail passengers in Great Britain. Trans. Res. Part A Policy Pract.
**2007**, 41, 107–120. [Google Scholar] [CrossRef][Green Version] - Ohmori, N.; Harata, N. How different are activities while commuting by train? A case in Tokyo. Tijdschr. Econ. Soc. Geogr.
**2008**, 99, 547–561. [Google Scholar] [CrossRef] - Ben-Akiva, M.; Bierlaire, M. Discrete Choice Methods and their Applications to Short Term Travel Decisions. In Handbook of Transportation Science; Hall, R.W., Ed.; Springer: Boston, MA, USA, 1999; pp. 5–33. [Google Scholar]
- Kitamura, R.; Mokhtarian, P.L.; Laidet, L. A micro-analysis of land use and travel in five neighborhoods in the San Francisco Bay Area. Transportation
**1997**, 24, 125–158. [Google Scholar] [CrossRef] - Handy, S.L.; Clifton, K.J. Local shopping as a strategy for reducing automobile travel. Transportation
**2001**, 28, 317–346. [Google Scholar] [CrossRef] - Bagley, M.N.; Mokhtarian, P.L. The impact of residential neighborhood type on travel behavior: A structural equations modeling approach. Ann. Reg. Sci.
**2002**, 36, 279–297. [Google Scholar] [CrossRef][Green Version] - Bhat, C.R.; Guo, J.Y. A comprehensive analysis of built environment characteristics on household residential choice and auto ownership levels. Trans. Res. Part B Methodol.
**2007**, 41, 506–526. [Google Scholar] [CrossRef][Green Version] - Cao, X.J.; Mokhtarian, P.L.; Handy, S.L. The relationship between the built environment and nonwork travel: A case study of Northern California. Trans. Res. Part A Policy Pract.
**2009**, 43, 548–559. [Google Scholar] [CrossRef] - Mokhtarian, P.L.; Cao, X. Examining the impacts of residential self-selection on travel behavior: A focus on methodologies. Trans. Res. Part B Methodol.
**2008**, 42, 204–228. [Google Scholar] [CrossRef][Green Version] - Krizek, K.J. Residential Relocation and Changes in Urban Travel: Does Neighborhood-Scale Urban Form Matter? J. Am. Plan. Assoc.
**2003**, 69, 265–281. [Google Scholar] [CrossRef] - Handy, S.; Cao, X.; Mokhtarian, P. Correlation or causality between the built environment and travel behavior? Evidence from Northern California. Trans. Res. Part D Trans. Environ.
**2005**, 10, 427–444. [Google Scholar] [CrossRef][Green Version] - Lynch, A.K.; Rasmussen, D.W. Measuring the impact of crime on house prices. Appl. Econ.
**2001**, 33, 1981–1989. [Google Scholar] [CrossRef] - Kuang, C. Does quality matter in local consumption amenities? An empirical investigation with Yelp. J. Urban Econ.
**2017**, 100, 1–18. [Google Scholar] [CrossRef] - Rappaport, J. Consumption amenities and city population density. Reg. Sci. Urban Econ.
**2008**, 38, 533–552. [Google Scholar] [CrossRef] - Pope, D.G.; Pope, J.C. When Walmart comes to town: Always low housing prices? Always? J. Urban Econ.
**2015**, 87, 1–13. [Google Scholar] [CrossRef][Green Version] - Jim, C.; Chen, W.Y. External effects of neighbourhood parks and landscape elements on high-rise residential value. Land Use Policy
**2010**, 27, 662–670. [Google Scholar] [CrossRef] - Kan, K. Residential mobility and social capital. J. Urban Econ.
**2007**, 61, 436–457. [Google Scholar] [CrossRef] - Gilderbloom, J.I.; Riggs, W.W.; Meares, W.L. Does walkability matter? An examination of walkability’s impact on housing values, foreclosures and crime. Cities
**2015**, 42, 13–24. [Google Scholar] [CrossRef] - Harrison, D.; Rubinfeld, D.L. Hedonic housing prices and the demand for clean air. J. Environ. Econ. Manag.
**1978**, 5, 81–102. [Google Scholar] [CrossRef] - Haase, D.; Lautenbach, S.; Seppelt, R. Modeling and simulating residential mobility in a shrinking city using an agent-based approach. Environ. Model. Softw.
**2010**, 25, 1225–1240. [Google Scholar] [CrossRef] - Krizek, K. Lifestyles, residential location decisions, and pedestrian and transit activity. Trans. Res. Rec. J. Trans. Res. Board
**2006**, 1981, 171–178. [Google Scholar] [CrossRef] - Ben-Akiva, M.; Bowman, J.L. Integration of an Activity-based Model System and a Residential Location Model. Urban Stud.
**1998**, 35, 1131–1153. [Google Scholar] [CrossRef] - Jacobs, J. The Death and Life of Great American Cities; Random House: New York, NY, USA, 1961. [Google Scholar]
- Walk Score. Available online: https://www.walkscore.com (accessed on 16 September 2018).
- Smith, C.; Quercia, D.; Capra, L. Finger on the Pulse: Identifying Deprivation Using Transit Flow Analysis. In Proceedings of the 2013 Conference on Computer Supported Cooperative Work, New York, NY, USA, 23–27 February 2013; pp. 683–692. [Google Scholar]
- Zhong, C.; Schläpfer, M.; Arisona, S.M.; Batty, M.; Ratti, C.; Schmitt, G. Revealing centrality in the spatial structure of cities from human activity patterns. Urban Stud.
**2017**, 54, 437–455. [Google Scholar] [CrossRef] - Yabe, T.; Tsubouchi, K.; Sekimoto, Y. CityFlowFragility: Measuring the Fragility of People Flow in Cities to Disasters Using GPS Data Collected from Smartphones. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol.
**2017**, 1, 117:1–117:17. [Google Scholar] [CrossRef] - Carpenter, B.; Gelman, A.; Hoffman, M.D.; Lee, D.; Goodrich, B.; Betancourt, M.; Brubaker, M.; Guo, J.; Li, P.; Riddell, A. Stan: A probabilistic programming language. J. Stat. Softw.
**2017**, 76. [Google Scholar] [CrossRef] - Hoffman, M.D.; Gelman, A. The No-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res.
**2014**, 15, 1593–1623. [Google Scholar] - Neal, R.M. MCMC Using Hamiltonian Dynamics. In Handbook of Markov Chain Monte Carlo; CRC Press: Boca Raton, FL, USA, 2010; Volume 54, pp. 113–162. [Google Scholar]
- Zipf, G.K. The P1P2/D Hypothesis: On the Intercity Movement of Persons. Am. Sociol. Rev.
**1946**, 11, 677–686. [Google Scholar] [CrossRef] - Gabaix, X. Zipf’s Law for Cities: An Explanation. Q. J. Econ.
**1999**, 114, 739–767. [Google Scholar] [CrossRef] - Moré, J.J. The Levenberg-Marquardt algorithm: Implementation and theory. In Numerical Analysis; Watson, G.A., Ed.; Springer: Berlin/Heidelberg, Germany, 1978; pp. 105–116. [Google Scholar]
- Shimizu, S.; Hoyer, P.O.; Hyvärinen, A.; Kerminen, A. A linear non-Gaussian acyclic model for causal discovery. J. Mach. Learn. Res.
**2006**, 7, 2003–2030. [Google Scholar] - Shapiro, S.S.; Wilk, M.B. An Analysis of Variance Test for Normality (Complete Samples). Biometrika
**1965**, 52, 591–611. [Google Scholar] [CrossRef] - Lee, B.H.Y.; Waddell, P. Residential mobility and location choice: a nested logit model with sampling of alternatives. Transportation
**2010**, 37, 587–601. [Google Scholar] [CrossRef][Green Version] - Neirotti, P.; Marco, A.D.; Cagliano, A.C.; Mangano, G.; Scorrano, F. Current trends in Smart City initiatives: Some stylised facts. Cities
**2014**, 38, 25–36. [Google Scholar] [CrossRef][Green Version] - Russo, F.; Rindone, C.; Panuccio, P. The process of smart city definition at an EU level. WIT Trans. Ecol. Environ.
**2014**, 191, 979–989. [Google Scholar]

**Figure 1.**Hypothesis on the causal directions between urban form, non-work human mobility and residential mobility.

**Figure 4.**Causal networks between the predictor using the opportunity cost of travel time (O), the predictor using population (P) and the number of residential moves to each place (M).

Age | 2016 | 2017 | ||
---|---|---|---|---|

Male | Female | Male | Female | |

0–9 | 11,331 | 12,274 | 12,252 | 13,308 |

10–19 | 127,968 | 141,913 | 133,691 | 147,673 |

20–29 | 146,365 | 215,936 | 148,487 | 217,400 |

30–39 | 198,082 | 251,226 | 193,508 | 248,822 |

40–49 | 275,129 | 310,716 | 279,966 | 322,486 |

50–59 | 219,646 | 225,320 | 230,026 | 242,502 |

60–69 | 143,823 | 151,027 | 157,696 | 169,407 |

70–79 | 133,427 | 182,992 | 130,555 | 180,812 |

80–89 | 40,429 | 53,125 | 43,489 | 58,318 |

90–99 | 1557 | 1840 | 1786 | 2083 |

Total | 1,297,757 | 1,546,369 | 1,331,456 | 1,602,811 |

**Table 2.**Correlation coefficients of the comparison of 24 wards in Osaka City between the population of smart card holders and the information about the demographic composition published by the government of Osaka City.

Age | 2016 | 2017 |
---|---|---|

0–9 | 0.787010 | 0.823162 |

10–19 | 0.937348 | 0.948269 |

20–29 | 0.958899 | 0.969244 |

30–39 | 0.935792 | 0.946171 |

40–49 | 0.925023 | 0.942998 |

50–59 | 0.927487 | 0.941806 |

60–69 | 0.897694 | 0.927388 |

70–79 | 0.950722 | 0.950101 |

80–89 | 0.948302 | 0.941291 |

90–99 | 0.882572 | 0.904075 |

Age | Male | Female |
---|---|---|

20–29 | 115,926 | 176,803 |

30–39 | 153,922 | 206,359 |

40–49 | 217,804 | 266,191 |

50–59 | 171,413 | 192,379 |

60–69 | 117,933 | 130,967 |

70–79 | 114,981 | 160,849 |

**Table 4.**Coefficients of determination (${R}^{2}$) between the number of people who relocate to each place (${m}_{i,k}$) and predicted numbers (${\phi}_{\mathrm{O}}$, ${\phi}_{\mathrm{P}}$, ${\phi}_{\mathrm{A}}$, ${\phi}_{\mathrm{E}}$).

Predictor | Male | Female | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | |

O (${\phi}_{\mathrm{O}}$) | 0.677131 | 0.682127 | 0.702986 | 0.686997 | 0.695490 | 0.677117 | 0.641250 | 0.685919 | 0.685707 | 0.669508 | 0.646802 | 0.621696 |

P (${\phi}_{\mathrm{P}}$) | 0.637419 | 0.625829 | 0.638509 | 0.627181 | 0.632797 | 0.662053 | 0.631902 | 0.654962 | 0.683051 | 0.662978 | 0.680595 | 0.693258 |

A (${\phi}_{\mathrm{A}}$) | 0.476285 | 0.462466 | 0.501236 | 0.484837 | 0.420105 | 0.397013 | 0.517185 | 0.459414 | 0.506208 | 0.459616 | 0.381638 | 0.390667 |

E (${\phi}_{\mathrm{E}}$) | 0.344690 | 0.337078 | 0.398216 | 0.410906 | 0.397417 | 0.230339 | 0.325484 | 0.344409 | 0.389053 | 0.372604 | 0.345309 | 0.227351 |

Valuable | Male | Female | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | |

O (${\phi}_{\mathrm{O}}$) | 1.18 × 10${}^{-25}$ | 9.34 × 10${}^{-28}$ | 5.78 × 10${}^{-25}$ | 9.99 × 10${}^{-23}$ | 1.59 × 10${}^{-24}$ | 9.59 × 10${}^{-32}$ | 1.04 × 10${}^{-25}$ | 1.45 × 10${}^{-27}$ | 9.53 × 10${}^{-24}$ | 5.21 × 10${}^{-24}$ | 9.02 × 10${}^{-25}$ | 2.44 × 10${}^{-30}$ |

P (${\phi}_{\mathrm{P}}$) | 7.73 × 10${}^{-27}$ | 5.09 × 10${}^{-28}$ | 1.13 × 10${}^{-26}$ | 6.38 × 10${}^{-26}$ | 9.00 × 10${}^{-27}$ | 1.46 × 10${}^{-31}$ | 5.26 × 10${}^{-28}$ | 1.93 × 10${}^{-28}$ | 9.89 × 10${}^{-28}$ | 5.59 × 10${}^{-28}$ | 3.06 × 10${}^{-29}$ | 4.13 × 10${}^{-32}$ |

M (${m}_{i,k}$) | 2.02 × 10${}^{-35}$ | 2.11 × 10${}^{-36}$ | 5.82 × 10${}^{-34}$ | 1.75 × 10${}^{-33}$ | 9.16 × 10${}^{-34}$ | 3.88 × 10${}^{-37}$ | 1.57 × 10${}^{-36}$ | 4.94 × 10${}^{-36}$ | 4.03 × 10${}^{-34}$ | 1.18 × 10${}^{-34}$ | 4.11 × 10${}^{-35}$ | 2.78 × 10${}^{-37}$ |

**Table 6.**Correlation coefficient (R) between the predictor using opportunity cost (${\phi}_{\mathrm{O}}$) and the predictor using current population (${\phi}_{\mathrm{P}}$).

Male | Female | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 |

0.827688 | 0.794022 | 0.783471 | 0.797551 | 0.805344 | 0.849521 | 0.823154 | 0.835350 | 0.816704 | 0.806756 | 0.813640 | 0.847267 |

**Table 7.**The reproducibility of causal networks obtained using LiNGAM: We repeat the experiment by making 1000 causal networks for each demographic group by randomly taking 400 departure places out of 599 departure places and making causal networks using the data of 400 departure places.

Direction of Causality | Male | Female | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | |

1: O to M, P to O, P to M | 1000 | 1000 | 1000 | 1000 | 1000 | 772 | 1000 | 1000 | 1000 | 1000 | 923 | 975 |

2: O to M, O to P, P to M | 0 | 0 | 0 | 0 | 0 | 228 | 0 | 0 | 0 | 0 | 77 | 19 |

3: O to P, M to O, M to P | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 6 |

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## Share and Cite

**MDPI and ACS Style**

Maeda, T.N.; Mori, J.; Ochi, M.; Sakimoto, T.; Sakata, I. Measurement of Opportunity Cost of Travel Time for Predicting Future Residential Mobility Based on the Smart Card Data of Public Transportation. *ISPRS Int. J. Geo-Inf.* **2018**, *7*, 416.
https://doi.org/10.3390/ijgi7110416

**AMA Style**

Maeda TN, Mori J, Ochi M, Sakimoto T, Sakata I. Measurement of Opportunity Cost of Travel Time for Predicting Future Residential Mobility Based on the Smart Card Data of Public Transportation. *ISPRS International Journal of Geo-Information*. 2018; 7(11):416.
https://doi.org/10.3390/ijgi7110416

**Chicago/Turabian Style**

Maeda, Takashi Nicholas, Junichiro Mori, Masanao Ochi, Tetsuo Sakimoto, and Ichiro Sakata. 2018. "Measurement of Opportunity Cost of Travel Time for Predicting Future Residential Mobility Based on the Smart Card Data of Public Transportation" *ISPRS International Journal of Geo-Information* 7, no. 11: 416.
https://doi.org/10.3390/ijgi7110416