Utility independence versus IIA property in independent probit models

Strategic sampling for large choice sets in estimation and application

Multinomial logit models and nested logit models are limited in that they cannot accommodate unobserved variations in travelers' taste and they do not have flexible substitution patterns among alternatives because of the independence of irrelevant alternatives property. Taking this background into account, traffic demand analysts have recently used the mixed logit model in many studies. Unfortunately, most of the studies in the literature for joint analysis of revealed-preference (RP) and stated-preference (SP) data could not simultaneously resolve the two limitations just mentioned. The mixed logit framework is used to formulate an intercity travel mode choice model for joint RP-SP analysis that accommodates the following behavioral considerations: ( a) observed and unobserved heterogeneity across individuals in response to level-of-service (LOS) factors, ( b) heteroscedasticity across alternatives, and ( c) scale differences between the RP and SP choice contexts. The mixed logit formulation is estimated with the maximum simulated likelihood method that employs quasi-random Halton draws. The formulation is applied to examine the travel behavior responses of users of the HoNam, South Korea, high-speed rail to changes in travel conditions. The empirical results show that there is a significant heteroscedasticity across alternatives and a significant heterogeneity in response to LOS attributes based on both observed and unobserved individual characteristics. There is an improvement in the data-fit statistics when one introduces heterogeneity and heteroscedasticity. These results highlight the need to include heterogeneity and heteroscedasticity within the context of intercity travel mode choice modeling to assist policy decision making.

Although the estimation of flexible multinomial discrete choice models generally needs the incorporation of simulation methods, their application is recently common in environmental and resource economics such as in many other economic disciplines (e.g. transportation economics). Based on a firm level data set of the German manufacturing sector, this paper examines determinants of environmental innovations by comparing the estimation results in flexible multinomial probit models and restrictive multinomial logit and independent probit models. The analysis of the two latter models implies that some specific environmental organizational measures, technological opportunities, and market pull factors have a significantly positive effect on both environmental product and process innovations. Taking this into consideration, the flexible multinomial probit model analysis provides few new insights since the simulated maximum likelihood estimations are rather unreliable as a consequence of the sole inclusion of firm-specific characteristics as explanatory variables. In this respect, the incorporation of simulation methods into the maximum likelihood estimations is not crucial since the problems do not decrease if the number of random draws in the considered Geweke-Hajivassiliou-Keane simulator rises. Furthermore, the difficulties grow if the number of choice alternatives increases. It can therefore be concluded that the applicability of these flexible multinomial discrete choice models without the incorporation of choice-specific attributes as explanatory variables is rather limited in practice.

Statisticians along with other scientists have made significant computational advances that enable the estimation of formerly complex statistical models. The Bayesian inference framework combined with Markov chain Monte Carlo estimation methods such as the Gibbs sampler enable the estimation of discrete choice models such as the multinomial logit (MNL) model. MNL models are frequently applied in transportation research to model choice outcomes such as mode, destination, or route choices or to model categorical outcomes such as crash outcomes. Recent developments allow for the modification of the potentially limiting assumptions of MNL such as the independence from irrelevant alternatives (IIA) property. However, relatively little transportation-related research has focused on Bayesian MNL models, the tractability of which is of great value to researchers and practitioners alike. This paper addresses MNL model specification issues in the Bayesian framework, such as the value of including prior information on parameters, allowing for nonlinear covariate effects, and extensions to random parameter models, so changing the usual limiting IIA assumption. This paper also provides an example that demonstrates, using route-choice data, the considerable potential of the Bayesian MNL approach with many transportation applications. This paper then concludes with a discussion of the pros and cons of this Bayesian approach and identifies when its application is worthwhile.

Covariance heterogeneity in nested logit models: Econometric structure and application to intercity travel

A comparative analysis of different specifications of modal choice models in an urban area

Bike-sharing systems (BSS) constitute a fundamental component of sustainable transportation development, significantly reducing the dependence on private vehicles, mitigating traffic congestion, and addressing environmental challenges in densely populated urban areas. This study develops a maximum capture problem designed to optimize bike lane network design, with the dual objective of maximizing user adoption and spatial equity by addressing disparities in service accessibility across diverse BSS station locations. The proposed problem employs the Multinomial Logit (MNL) travel choice behavior. The independence of irrelevant alternatives (IIA) property of used to provides a mixed-integer linear programming (MILP) formulation. Through numerical examples of the Chaing Mai transportation network, the proposed MILP can determine the bike lane network and BSS station location to optimize the number of users. Multimodal transport is a key factor in promoting BSS usage, where both the BSS and public transit gain win-win situations. Spatial equity and transportation network characteristics play significant roles in determining the optimum BSS station location. A unit change in the MNL dispersion parameter has a high impact on the bike modal shift, the spatial equity, and bike usage distance travelled.

This chapter continues with the multinomial logit model discussed in section 2.12. It derives the multinomial logit model from a theory of probabilistic choice. We then discuss its limitations and examine some extensions of this model (the multinomial probit model, the nested logit model, the generalized extreme-value model, etc.). McFadden's conditional logit model In the previous chapter we discussed the multinomial logit model as an extension of the simple logit model for dichotomous variables. There it was pointed out that there is a difference in the way the multinomial logit model was derived and discussed in some of the statistical literature and the way it was discussed by McFadden. The latter discussion is related to the hedonic-price problem in econometrics and the theory of probabilistic choice discussed by several psychologists. In this chapter we shall discuss the multinomial logit model and its extensions as developed by McFadden (1973, 1974, 1976 a , 1978, 1979, 1982, in press). We start with the assumption that consumers are rational in the sense that they make choices that maximize their perceived utility subject to constraints on expenditures. However, there are many errors in this maximization because of imperfect perception and optimization, as well as the inability of the analyst to measure exactly all the relevant variables. Hence, following Thurstone (1927), McFadden assumed that utility is a random function.

The most commonly used variant of conjoint analysis is choice-based conjoint (CBC). Here, hierarchical Bayesian (HB) multinomial logit (MNL) models are widely used for preference estimation at the individual respondent level. A new and very flexible approach to address multimodal and skewed preference heterogeneity in the context of CBC is the Dirichlet Process Mixture (DPM) MNL model. The number and masses of components do not have to be predisposed like in the latent class (LC) MNL model or in the mixture-of-normals (MoN) MNL model. The aim of this Monte Carlo study is to evaluate the performance of Bayesian choice models (basic MNL, HB-MNL, MoN-MNL, LC-MNL and DPM-MNL models) under varying data conditions (especially under multimodal heterogeneity structures) using statistical criteria for parameter recovery, goodness-of-fit and predictive accuracy. The core finding from this Monte Carlo study is that the standard HB-MNL model appears to be highly robust in multimodal preference settings.

Activity and purpose based trip making studies are gaining popularity in current transportation research industry. The purpose is determined by activity one is to engage in at the destination of the trip. The trip purpose can be influenced by many socioeconomic factors. Based on the importance of determining the effect of trip purpose, this study applies a multinomial modeling approach to evaluate various factors which determine purpose based trips. The study utilizes trip data from the 2001 National Household Travel Survey (NHTS). Home based and non-home based work, school, shopping, family, social and religious driven trips are modeled by using different socioeconomic variables. Multinomial logit (MNL) and multinomial probit (MNP) models are used in this study in determining the effect of the variables.

Mode choice behaviour is often modelled by discrete choice models, in which the utility of each mode is characterized by mode-specific parameters reflecting how strongly the utility of that mode depends on attributes such as travel speed and cost, and a mode-specific constant value. For new modes, the mode-specific parameters and the constant in the utility function of discrete choice models are not known and are difficult to estimate on the basis of stated preferences data/choice experiments and cannot be estimated on the basis of revealed preference data. This paper demonstrates how revealed preference data can be used to estimate a discrete mode choice model without using mode-specific constants and mode-specific parameters. This establishes a method that can be used to analyze any new mode using revealed preference data and discrete choice models and is demonstrated using the OViN 2017 dataset with trips throughout the Netherlands using a multinomial and nested logit model. This results in a utility function without any alternative specific constants or parameters, with a rho-squared of 0.828 and an accuracy of 0.758. The parameters from this model are used to calculate the future modal split of shared autonomous vehicles and electric steps, leading to a potential modal split range of 24–30% and 37–44% when using a multinomial logit model, and 15–20% and 33–40% when using a nested logit model. An overestimation of the future modal split occurs due to the partial similarities between different transport modes when using a multinomial logit model. It can therefore be concluded that a nested logit model is better suited for estimating the potential modal split of a future mode than a multinomial logit model. To the authors’ knowledge, this is the first time that the future modal split of shared autonomous vehicles and electric steps has been calculated using revealed preference data from existing modes using an unlabelled mode modelling approach.

Efficient estimation of probit models with correlated errors

Over the years, researchers have been studying the effects of weather and context data on transport mode choices. Existing research studies are predominantly designed around travel surveys, but the accuracy of their findings relies on how travelers give accurate and honest answers. The proliferation of smartphones, however, now offers the possibility of utilizing GPS positioning data as an alternative information source, opening the potential to accurately model and better understand factors which influence transport mode choices, compared to travel surveys. The objective of this work is to develop a model to predict the transport mode choices based on GPS trajectories, weather and context data. We use 2671 GPS trajectories from the Geolife GPS trajectories dataset, weather data, such as temperature and air quality, and context data, such as rush hour, day/night time and onetime events, such as the Olympics. In the statistical analysis, we apply both descriptive and statistical models, such as the multinomial logit and probit models. We find that temperature has the most prominent effect among weather conditions. For instance, for temperatures greater than 25 °C, the walking share increases by 27%, and the bike share reduces by 21%, which is line with the results from several survey-based studies. In addition, the evidence of government policy on transport regulation is revealed when the air quality becomes hazardous, as people are encouraged to use environmentally friendly transport mode choices, such as the bike instead of the bus or car, which are known CO2 emitters. Our conclusion is that GPS trajectories can be used as a means to model passenger behavior, e.g. the choice of transport mode, in a quantitative way, which will support transport mode operators and policy makers in their efforts to design and plan the transport mode infrastructure to best suit the passengers’ needs.

A generalized multinomial logit (G-MNL) model is proposed to alleviate the four challenges inherent to the conditional logit model, including (1) simultaneous unidentifiability, (2) the immediacy of decision-making, (3) the homogeneity of preferences in unobservable variables, and (4) the independence of irrelevant alternatives. However, the G-MNL model has some restrictions that are caused by the assumed logit scale of the lognormal distribution used in the G-MNL model. We propose a mixed logit with integrated Pareto-distributed scale (MIXL-iPS) model to address the restriction of the G-MNL model by introducing a logit scale in accordance with the Pareto distribution type I with an expected value of 1. We have clarified the mathematical properties and examined the distributional properties of the novel MIXL-iPS model. The results suggest that the MIXL-iPS model is a model in which the instability in the estimation of the G-MNL model is modified. Moreover, the apparent preference parameter was confirmed to have a skewed distribution in general in the MIXL-iPS model. In addition, we confirm that in the MIXL-iPS model, bounded rationality is reasonably well represented, as many individuals have below-average choice consistency.

Although formal conditions for identification in the multinomial probit (MNP) model are now clearly established, little is known about how various estimable MNP specifications perform in practice. This article shows that parameter identification in the MNP model is extremely tenuous in the absence of exclusion restrictions. This previously unnoticed fact is important because formal identification of MNP models does not require exclusion restrictions, and many potential economic applications of MNP are to situations in which exclusion restrictions are not readily available. Thus, failure to be aware of the difficulties present in such situations may lead to reporting of unreliable results.