Juan de Dios Ortúzar

Willingness-to-Pay Estimation with Mixed Logit Models: Some New Evidence

Mixed-logit models are currently the state of the art in discrete-choice modelling, and their estimation in various forms (in particular, mixing revealed-preference and stated-preference data) is becoming increasingly popular. Although the theory behind these models is fairly simple, the practical problems associated with their estimation with empirical data are still relatively unknown and certainly not solved to everybodys satisfaction. In this paper we use a stated-preference dataset—previously used to derive willingness to pay for reduction in atmospheric pollution and subjective values of time—to estimate random parameter mixed logit models with different estimation methods. We use our results to discuss in some depth the problems associated with the derivation of willingness to pay with this class of models.

Estimating demand for a cycle-way network

We study the use of bicycles as an alternative mode of transport in Santiago. We consider the incorporation of a dense network of cycle-ways, fully segregated from motorised traffic, and the inclusion of adequate bicycle shelter facilities at Metro, suburban train and selected segregated bus-way stations. We designed and applied a methodology which included: (i) a review of national and international experience; (ii) focus group surveys; (iii) a household survey including stated preference experiments for potential bicycle users; (iv) estimation of various models with this data, and (v) model application using extra data available for the whole of the city. Our results indicate that there are sectors of the city where bikes could capture more than 10% of the trips, and that, on average, the use of bicycles could jump from its current 1.6% to approximately 5.8%. Finally, our results also show clearly that trip length is a fundamental variable; therefore, land use policies geared to the development of urban sub-centres could have a significant impact in the future of this clean and efficient mode of transport.

Willingness-to-pay for reducing fatal accident risk in urban areas: an Internet-based Web page stated preference survey

Contemporary transport project evaluation requires the ability to value reductions in the number of estimated fatal and non-fatal accidents after project implementation. In this quest, we designed a stated preference (SP) experiment to estimate willingness-to-pay (WTP) for reducing fatal accident risk in urban areas. The survey was implemented in a Web page allowing rapid turnover and a complete customisation of the interview. The sample was presented with a series of route choice situations based on travel time, cost and number of car fatal accidents per year. With this data we estimated Multinomial Logit (MNL) and Mixed Logit (ML) models based on a consistent microeconomic framework; the former with linear and non-linear utility specifications and allowing for various stratifications of the data. The more flexible ML models also allow to treat the repeated observations problem common to SP data and, as expected, gave a better fit to the data in all cases. Based on these models, we estimated subjective values of time, that were consistent with previous values obtained in the country, and also sensible values for the WTP for reductions in fatal accident risk. Thus, the Internet appears as a potentially very interesting medium to carry out complex stated choice surveys.

VALUE OF TIME SENSITIVITY TO MODEL SPECIFICATION

We compare values of time obtained with linear utility functions used in LOGIT and HIERARCHICAL LOGIT specifications of a nine-mode passenger choice model estimated with disaggregate data from Santiago, Chile, and find that they are sensitive to the specification used, unconvincingly high, and imply that the value of waiting time is a decreasing function of income. We then find that removing observations for individuals who face limiting values of price or service level yields partially improved results if the utility functions are still linear; but the most convincing results are obtained with explicitly nonlinear BOX-COX LOGIT specifications.

CONFIDENCE INTERVALS TO BOUND THE VALUE OF TIME

Abstract The derivation of a subjective value of time (SVT) requires finding the marginal rate of substitution between travel time and cost in a travel choice model. In the typical case of models with linear-in-parameters utility functions, the SVT is equal to the ratio between the parameters of travel time and cost. However, since model estimation yields an estimator of the true values of their parameters (with a certain probability distribution), the computed SVT is also an estimator with another probability distribution; then, it is important to devise a method to incorporate the randomness of the estimated SVT in project evaluation. In this paper, we consider this problem rigorously and propose methods to replace the typical SVT point estimates by the construction of confidence intervals for a certain probability level. This allows, in addition, to estimate the SVT limits (lower and upper) which may be used in sensitivity analyses of the calculation of project revenues in transport infrastructure investment. The paper proposes two forms for building these intervals: the t -test and the LR-test, and discusses the construction of intervals for Multinomial Logit (MNL), Hierarchical Logit (HL) and Box–Cox Logit (BCL) models. We use two samples where the values of the level-of-service attributes have been measured with an unusually high degree of precision. Other methods proposed in the literature are also studied (simulation of multivariate normal variates (MVNS), SVT normal approximation (NA), and re-sampling techniques) using the above data, and their advantages and disadvantages are analysed. In addition, the effects of different modelling elements on the size and quality of the constructed intervals are scrutinised, such as model specification, sample size and individual income. Finally, the proposed methods are compared and recommendations about the use of each one in practice are indicated.

Modeling Discrete Choices in the Presence of Inertia and Serial Correlation

The concept of habit or inertia in the context of (reluctance to) change in travel behavior has an important bearing on transport policy (e.g., how to break car use habits) and has remained an unresolved issue in demand modeling. Another major problem in modeling the response to policy measures is the potential correlation or dependence between the choices made by a given individual over time (i.e., serial correlation). The two phenomena are closely related. This paper discusses the effects of considering inertia and serial correlation on travel choices. We formulate a fairly general discrete choice model that incorporates randomly distributed inertia thresholds and allow for serial correlation. The inertia thresholds may also be a function of an individuals socioeconomic characteristics and choice conditions. The model can be applied with panel data as well as with mixed revealed and stated preference data. We applied it to real and simulated data, confirming that if these phenomena exist in the population but are not considered, serious errors in model estimation and prediction may arise, especially in the case of large policy impacts.

Sequential and Simultaneous Estimation of Hybrid Discrete Choice Models: Some New Findings

The formulation of hybrid discrete choice models, including both observable alternative attributes and latent variables associated with attitudes and perceptions, has become a topic of discussion once more. To estimate models integrating both kinds of variables, two methods have been proposed: the sequential approach, in which the latent variables are built before their integration with the traditional explanatory variables in the choice model and the simultaneous approach, in which both processes are done together, albeit with a sophisticated but fairly complex treatment. Here both approaches are applied to estimate hybrid choice models by using two data sets: one from the Santiago Panel (an urban mode choice context with many alternatives) and another consisting of synthetic data. Differences between both approaches were found as well as similarities not found in earlier studies. Even when both approaches result in unbiased estimators, problems arise when valuations are obtained such as the value of time for forecasting and policy evaluation.

Mixed RP/SP models incorporating interaction effects

In order to analyse the impact of a new train service in Cagliari (Italy) a databank including information from a revealed preference (RP) and a stated preference (SP) survey was set up. The RP data concern choice between car, bus and train; the SP data consider the binary choice between a new train service (quicker, more frequent, with a lower fare and more stations than the current one) and the alternative currently chosen by car and bus users. Logit models allowing for correlation among RP alternatives were estimated for this mixed RP/SP data set using the artificial tree structure method. The analysis included level-of-service variables measured with an unusually high level of precision, latent or second order variables (such as comfort), inertia and interaction variables. Different specifications of the utility function were tested, including the expenditure rate model, and the effects of these specifications on modelling results are highlighted. Our results show that for a population mainly composed of fixed income workers, the expenditure rate model is superior to the traditional wage rate model, yielding lower and more significant subjective values of time. Moreover, we found that the non-linear specifications appear to be more suitable as not only better model results were obtained, but also the real distribution of the error terms was revealed (i.e. highlighting correlation among public transport options).

Nested logit models for mixed-mode travel in urban corridors

Abstract The nested logit (NL) model is a generalisation of the well-known multinomial logit (MNL) model which copes with its “independence from irrelevant alternatives” problem, at the expense of more difficult calibration and use. Mixed-mode movements (i.e. park-and-ride) are by nature not independent of competing single-mode options and have, therefore, traditionally been inadequately modelled in most empirical applications. This paper reports on the specification, estimation, testing and comparison of MNL and NL models using disaggregate data of work trips in an urban corridor, where choice was among several alternatives including mixed-mode options. It was found that the more general NL model was more adequate, not only in theory but in practice. The paper concludes by comparing the disaggregate NL model with previously calibrated aggregate NL models for the same corridor using a different data set.

Review and assessment of the nested logit model

The popular hierarchical or nested logit model that has been the recent source of heated discussions in the literature is reviewed and critically examined. The fundamental underpinnings of the model are first presented in a concise and easy-to-understand fashion and then used to assess each controversy in turn. Monte Carlo simulation is also used to examine some problems that are not possible to address by just resorting to the theory. The main conclusion is that all the model hypotheses are both essential and unambiguous and should not be ignored for a correct use of the model in practice.