Abstract
Panel data offers the potential to represent the influence on travel choices of changing circumstances, past history and persistent individual differences (unobserved heterogeneity). A four-wave panel survey collected data on the travel choices of residents before and after the introduction of a new bus rapid transit service. The data shows gradual changes to bus use over the four waves, implying time was required for residents to become aware of the new service and to adapt to it. Ordered response models are estimated for bus use over the survey period. The results show that the influence of level of service (LOS) is underestimated if unobserved heterogeneity is not taken into account. The delayed response to the new service is able to be well represented by including LOS as a lagged variable. Current bus use is found to be conditioned on past bus use, but with additional influence of lagged LOS and unobserved heterogeneity. It is shown how different model specifications generate different evolution patterns with the most realistic predictions arising from a model which takes into account lagged responses to change in LOS and unobserved heterogeneity. The paper demonstrates the feasibility of developing panel data models that can be applied to forecasting the effect of interventions in the travel environment. Longer panels—encompassing periods of both stability and change—are required to support future efforts at modelling travel choice dynamics.
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Notes
Stated choice surveys can also be used to collect multiple observations of \( y_{it}^{*} \) for the same individuals with experimenter-specified values for x it (representing hypothetical policy scenarios). This provides within-person variation in choices but the time frame in which choices are made is ambiguous.
Models which predict the dependent variable as a weighted function of present and past values of explanatory variables are called distributed-lag models (Grilliches 1967).
Serial correlation is specified by specifying ε it = ρε it + ζit, where ρ is the correlation and ζit is a random error term that is independent and identically distributed.
The assumption of independence between α i and x it is questionable and can introduce omitted-variable bias. Following Mundlak (1978) it is customary to parameterize the individual effect as a linear function of the mean of time varying independent variables as follows: \( \alpha_{i} = \alpha \bar{x}_{i} + \eta_{i} \) where \( \bar{x}_{i} \) is mean of time varying independent variables (instrumental variables), α is a vector of estimable parameters and ηi is independent of x it . Correction for correlation between α i and x it is not shown in the subsequent model specifications but was tested for all random effects models and not found to be required.
Roy et al. (1996) found that serial correlation was not statistically significant after state dependence and unobserved heterogeneity were included in panel data models for ketchup purchasing.
Generalized residual is calculated as: e i = (2y i1 − 1)φ(λ′z i )/Φ({2y i1 − 1}λ′z i ) where φ and Φ are the normal density and distribution functions respectively and λ′ are estimated values of parameters in Eq. 8.
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Acknowledgments
The research reported in this paper was funded by a grant from the UK Engineering and Physical Sciences Research Council (EPSRC). The author wishes to thank his former colleague, Dr Kang-Rae Ma (Chung-Ang University, Korea), for his contribution to the research and his colleague, Professor Phil Goodwin, for useful discussions about the data analysis.
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Chatterjee, K. Modelling the dynamics of bus use in a changing travel environment using panel data. Transportation 38, 487–509 (2011). https://doi.org/10.1007/s11116-010-9312-y
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DOI: https://doi.org/10.1007/s11116-010-9312-y