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A random heaping model of annual vehicle kilometres travelled considering heterogeneous approximation in reporting

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Abstract

Annual vehicle kilometres travelled (VKT) is a long used index of car use. Usually, the annual VKT, as reported by respondents, is used for the analysis. But the reported values almost systematically contain approximations such as rounding and heaping. We apply a latent class approach in modelling VKT to account for this problem developed by Heitjan and Rubin (J Am Stat Assoc 85(410):304–314, 1990; Ann Stat 19(4):2244–2253, 1991). Our model takes the form of a mixture of ordered probit models. The level of coarseness in reporting is considered as a latent variable that determines a category the respondent may belong to. Ordered response probit models of VKT are developed for each category. Thresholds are predetermined and model the level of coarseness that relates to the category. Annual VKT is itself assumed to affect the level of coarseness in reporting, thus included as an explanatory variable of the latent coarseness model. It is also modelled by an ordered probit model. The data set used in this study is a panel data of French households’ vehicle ownership (Parc-Auto panel survey). The results confirm that the longer VKT results in a larger coarseness in the report. The results also suggest that the coarseness in the report of VKT is larger for commuting car than others. The coefficient estimates on the VKT function are not statistically different from those estimated by conventional regression model of VKT. However, the estimated variance of the error term and the standard errors of the coefficient estimates in the VKT function for the proposed model are smaller than those for conventional regression model, implying that the proposed model is more efficient to investigate the effect of the explanatory variables on VKT than the conventional regression model.

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Notes

  1. Indeed, one could see in the log-likelihood shown in Eq. 8 that, for given values of β and σε, there are several candidates for {α; σεζ} leading to the same correlation value in the third term of Φ2. For each of these α candidates, γ can then be adjusted so as to yield the same value in the second argument of Φ2 if the covariates xi in the mileage equation are all included in the coarseness equation, resulting in this case in an identification issue.

  2. 79 observations over 2257 in the dataset.

  3. Despite appearances, this conclusion is not inconsistent with the expected tail-off in car use on the last part of life cycle: while retired drivers over 60 years old do not use their car anymore to commute, the induced decrease in car use is here captured by the "commuting car" dummy in the VKT function.

  4. The estimated standard deviations are 0.644, 0.620, 0.590 and 0.544 for predetermined coarseness levels of 500 km, 1000 km, 5000 km and 10,000 km respectively.

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Acknowledgements

An earlier version of this study was presented at the 12th International Conference on Travel Behaviour Research. Since then, the data set was updated and the models have been re-estimated with the newer data. The data set used in the empirical analysis of this study was provided by KANTAR-SOFRES, and the survey was funded by ADEME (Agency for Environment and Energy Savings) and CCFA (Committee of French Car Manufacturers). The comments by anonymous reviewers were very helpful to improve the presentation of the study. The authors also thank Noritaka Nakagawa who provided computational assistance.

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Authors and Affiliations

  1. Institute of Materials and Systems for Sustainability, Nagoya University, C1-3(651) Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan

    Toshiyuki Yamamoto

  2. Laboratory of Economic and Social Dynamics of Transports (DEST), AME/IFSTTAR, French Institute of Science and Technology for Transport, Development and Networks, 14-20 Boulevard Newton B524, Cité Descartes, Champs-sur-Marne, 77447, Marne la Vallée Cedex 2, France

    Jean-Loup Madre & Roger Collet

  3. School of Engineering and Management Vaud (HEIG-VD), University of Applied Sciences and Arts of Western Switzerland (HES-SO), Avenue des Sports 20, 1401, Yverdon-les-Bains, Switzerland

    Matthieu de Lapparent

Authors
  1. Toshiyuki Yamamoto
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  2. Jean-Loup Madre
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  3. Matthieu de Lapparent
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  4. Roger Collet
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Contributions

TY: Conceptualization, literature review, model estimation, manuscript writing and editing. J-LM: Data preparation, manuscript writing and editing. ML: Manuscript writing and editing. RC: Data preparation, model estimation, manuscript writing and editing.

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Correspondence to Toshiyuki Yamamoto.

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Yamamoto, T., Madre, JL., de Lapparent, M. et al. A random heaping model of annual vehicle kilometres travelled considering heterogeneous approximation in reporting. Transportation 47, 1027–1045 (2020). https://doi.org/10.1007/s11116-018-9933-0

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