Abstract
In the face of growing concerns about greenhouse gas emissions, there is increasing interest in forecasting the likely demand for alternative fuel vehicles. This paper presents an analysis carried out on stated preference survey data on California consumer responses to a joint vehicle type choice and fuel type choice experiment. Our study recognises the fact that this choice process potentially involves high correlations that an analyst may not be able to adequately represent in the modelled utility components. We further hypothesise that a cross-nested logit structure can capture more of the correlation patterns than the standard nested logit model structure in such a multi-dimensional choice process. Our empirical analysis and a brief forecasting exercise produce evidence to support these assertions. The implications of these findings extend beyond the context of the demand for alternative fuel vehicles to the analysis of multi-dimensional choice processes in general. Finally, an extension verifies that further gains can be made by using mixed GEV structures, allowing for random heterogeneity in addition to the flexible correlation structures.
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Notes
We calculated the base price for used vehicles by taking a new vehicle price for that specific vehicle class and fuel type and depreciating it over the age of the vehicle using depreciation rates provided by the Energy Commission.
Below $20,000; between $20,000 and $40,000; between $40,000 and $60,000; between $60,000 and $80,000; between $80,000 and $100,000; between $100,000 and $120,000; and above $120,000.
With V i giving the modelled utility of alternative i out of J alternatives, the MNL probability of choosing alternative i is given by \( P_{i} = \frac{{e^{{V_{i} }} }}{{\mathop \sum \nolimits_{j = 1}^{J} e^{{V_{j} }} }} \). Here, V i is a function of the attributes of alternative i and estimated parameters which include the various constants and marginal utility coefficients listed above.
In a two-level NL model with M different nests, where \( j \in S_{m} \) defines the set of alternatives contained in nest m, the probability of choosing alternative i (where i is contained in nest k) is given by \( P_{i} = \frac{{e^{{\lambda_{k} I_{k} }} }}{{\sum_{m = 1}^{M} e^{{\lambda_{m} I_{m} }}}}\frac{{e^{{V_{j}}/\lambda_{k}}}}{{\sum_{{j \in S_{k} }}e^{{{{V_{j}}/\lambda_{k}}}} }} \), with \( I_{k} = \ln \mathop \sum \limits_{{j \in S_{k} }}e^{{{V_{j}}/\lambda_{k}}}.\)
In the present paper, the general specification also given in Train (2003) is used. Again using different nests, with α jm describing the allocation of alternative j to nest m, we have that
\( P_{i} = \sum_{m = 1}^{M} \left( {\frac{{\left( { \sum \nolimits_{{j \in S_{m} }} \left( {\alpha_{jm} e^{Vj} }\right)^{{1/\lambda_{m}}}} \right)^{{\lambda_{m} }} }}{{ \sum \limits_{l = 1}^{M} \left( { \sum_{{j \in S_{l} }} \left({\alpha_{jl} e^{Vj} } \right)^{1/\lambda_{l}}}\right)^{{\lambda_{l} }} }}\frac{{\left( {\alpha_{im} e^{Vi} }\right)^{{1/\lambda_{m}}}}}{{ \sum_{j = 1}^{J} \left( {\alpha_{jm}e^{Vj} } \right)^{{1/\lambda_{m}}}}}} \right). \) Here, the extra summation in comparison with the NL formula ensures that each alternative can potentially belong to each nest. In the present specification, we have two conditions for the allocation parameters, namely \( 0 \le \alpha_{jm} \le 1, \forall j,m \), and \( \sum\nolimits_{m = 1}^{m = 1} {\alpha_{jm} = 1} , \forall j. \)
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Acknowledgments
This paper uses data collected for a project commissioned by the California Energy Commission. The opinions expressed in this paper are those of the authors and do not necessarily reflect the views or policies of the California Energy Commission. The first author acknowledges the financial support of the Leverhulme Trust in the form of a Leverhulme Early Career Fellowship.
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Hess, S., Fowler, M., Adler, T. et al. A joint model for vehicle type and fuel type choice: evidence from a cross-nested logit study. Transportation 39, 593–625 (2012). https://doi.org/10.1007/s11116-011-9366-5
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DOI: https://doi.org/10.1007/s11116-011-9366-5