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

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.