# 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 |

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**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