Discrete choice theory, information theory and the multinomial logit and gravity models

Understanding and forecasting complex freight mode choice behavior under various industry, policy, and technology contexts is essential for freight planning and policymaking. Numerous models have been developed to provide insights into freight mode selection; most use discrete choice models such as multinomial logit (MNL) models. However, logit models often rely on linear specifications of independent variables despite potential nonlinear relationships in the data. A common challenge for researchers is the absence of a heuristic and efficient method to discern and define these complex relationships in logit model specifications. This often results in models that might be deficient in both predictive power and interpretability. To bridge this gap, we develop an MNL model for freight mode choice using the insights from machine learning (ML) models. ML models can better capture the nonlinear nature of many decision-making processes, and recent advances in “explainable AI” have greatly improved their interpretability. We showcase how interpretable ML methods help enhance the performance of MNL models and deepen our understanding of freight mode choice. Specifically, we apply SHapley Additive exPlanations (SHAP) to identify influential features and complex relationships to improve the MNL model’s performance. We evaluate this approach through a case study for Austin, Texas, where SHAP results reveal multiple important nonlinear relationships. Incorporating those relationships into MNL model specifications improves the interpretability and accuracy of the MNL model. Findings from this study can be used to guide freight planning and inform policymakers about how key factors affect freight decision-making.

Entropy, spatial interaction models and discrete choice analysis: Static and dynamic analogies

This chapter gives an overviewof the content of the book. The book deals with a new approach to logit type discrete choice probability models – for transportation networks in particular. The models are derived from a new definition of cost-minimizing behavior – the likelihood of a sample is decreasing as a function of average cost. The formal definitions are given in Chap. 4: Definition 1 (multinomial logit model) and Definition 4 (general logit model). The results for the multinomial logit model and the general logit model are obtained in Propositions 1 and 3 respectively. All logit type choice probability functions satisfy the new definition. The new definition is in Part I applied to networks with constant link costs. It is shown that the simple (multinomial) logit model exhibits cost-minimizing behavior. Furthermore cost-minimizing behavior implies the logit model. A number of standard logit models are derived – stochastic route choice model, multi-attribute discrete choice model, gravity model and the general logit model. New structured logit models, different from the standard nested logit model, are obtained. A welfare measure based on cost and a measure of freedom of choice is given. The new welfare measure is shown to be identical with composite cost. The presence of cost-minimizing behavior in an observed data set can be investigated by using the property that the likelihood is decreasing as a function of average cost. This is used in constructing a graphical test for cost-minimizing behavior. In Part II of the book the new definition of cost-minimizing behavior is extended to the case of volume dependent separable link costs. Here equilibrium is studied. Cost-minimizing behavior implies that the most probable trip patterns are user equilibria. The most probable flow patterns are approximately obtained by solving the optimization problem obtained by relaxing the integer constraints and replacing the cumulative cost function with the Beckmann integral.Models are derived for route choice, combined choice of origin, destination and route as well as combined choice of origin, destination, mode and route.KeywordsLogit ModelAverage CostRoute ChoiceChoice ProbabilityUser EquilibriumThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior

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.

Errors in variables in multinomial choice modeling: A simulation study applied to a multinomial logit model of travel mode choice

The multinomial logit (MNL) model and its variations have been dominating the travel mode choice modeling field for decades. Advantages of the MNL model include its elegant closed-form mathematical structure and its interpretable model estimation results based on random utility theory, while its main limitation is the strict statistical assumptions. Recent computational advancement has allowed easier application of machine learning models to travel behavior analysis, though research in this field is not thorough or conclusive. In this paper, we explore the application of the extreme gradient boosting (XGB) model to travel mode choice modeling and compare the result with an MNL model, using the Delaware Valley 2012 regional household travel survey data. The XGB model is an ensemble method based on the decision-tree algorithm and it has recently received a great deal of attention and use because of its high machine learning performance. The modeling and predicting results of the XGB model and the MNL model are compared by examining their multi-class predictive errors. We found that the XGB model has overall higher prediction accuracy than the MNL model especially when the dataset is not extremely unbalanced. The MNL model has great explanatory power and it also displays strong consistency between training and testing errors. Multiple trip characteristics, socio-demographic traits, and built-environment variables are found to be significantly associated with people’s mode choices in the region, but mode-specific travel time is found to be the most determinant factor for mode choice.

Investigating hazardous factors affecting freeway crash injury severity incorporating real-time weather data: Using a Bayesian multinomial logit model with conditional autoregressive priors

Multinomial logit (MNL) models have been applied extensively in transportation engineering, marketing, and recreational demand modeling. Thus far, this type of model has not been used to estimate the proportion of crashes by collision type. This study investigated the applicability of MNL models to predict the proportion of crashes by collision type and to estimate crash counts by collision type. MNL models were compared with two other methods described in recent publications to estimate crash counts by collision type: (a) fixed proportions of crash counts for all collision types and (b) collision type models. This study employed data collected between 2002 and 2006 on crashes that occurred on rural, two-lane, undivided highway segments in Minnesota. The study results showed that the MNL model could be used to predict the proportion of crashes by collision type, at least for the data set used. Furthermore, the method based on the MNL model was found useful to estimate crash counts by collision type, and it performed better than the method based on the use of fixed proportions. The use of collision type models, however, was still found to be the best way to estimate crash counts by specific collision type. In cases where collision type models are affected by the small sample size and a low sample-mean problem, the method based on the MNL model is recommended.

Discrete choice experiments have proven useful in areas such as marketing, government planning, medical studies and psychological research, to help understand consumer preferences. To aid in these experiments, several groups of authors have contributed to the theoretical development of D-optimal and A-optimal discrete choice designs under the multinomial logit (MNL) model. In the setting in which the class of feasible designs is too large for complete search, Sun and Dean (J Stat Plann Inference 170:144–157, 2016) proposed a construction method for A-optimal designs for estimating a set of orthonormal contrasts in the option utilities via a linearization of the MNL model. In this paper, we show that the set of A-optimal designs that result from this linearization may or may not include the optimal design under the MNL model itself. We provide an alternative linearization that leads to an information matrix which coincides with that under the MNL model and, consequently, selects the same set of designs as being A-optimal. We obtain a bound for the average variance of a set of contrasts of interest under the MNL model, and show that the construction method of Sun and Dean (2016) can be used to identify A-optimal and A-efficient designs under the MNL model for both equal and unequal utilities.

Most choice models, e.g. Multinomial Logit (MNL), rely on random utility theory, which assumes that a compensatory utility maximization decision rule explains an individual’s choice behaviour. Research has shown, however, that behaviour is sometimes better explained by non-compensatory decision rules. While some research has used Latent Class Choice Models (LCCMs) to account for multiple decision rules, many of them – such as the disjunctive rule – have yet to be explored. This paper formulates, estimates, and evaluates a LCCM that combines the MNL with a Generalised Random Disjunctive Model (GRDM), a new choice model we develop. Addressing deficiencies of existing disjunctive choice models, the GRDM allows for relative importance between attributes and is insensitive to irrelevant attributes. Unlike most non-compensatory models, it is tractable and incorporates random error terms for capturing unobserved heterogeneity across choice situations. The GRDM can be expressed as a Universal Logit (UL) model, which helps derive welfare metrics such as Marginal Rates of Substitution and elasticities and makes it possible to estimate the model with traditional software packages. The LCCM combining the GRDM and the MNL is estimated in two large-scale case studies: cyclists’ route choice and public transport route choice. Results are compared with other relevant LCCM specifications and the individual choice models, where it is found that the MNL + GRDM LCCM provides the best fit to the data. We also interpret the fitted parameters and calculate the Marginal Rates of Substitution, which align with behavioural expectations.

This paper investigates the effect of climate change on crop and livestock choices using two discrete choice models: Multinomial Logit (MNL) and Nested Logit (NL) models. Taking advantage of a new-plot level dataset for Mexico we identify the effect of climate on agriculturalists observed choices. Using Geographical Information Systems (GIS) we combine data on 31 types of crops and livestock encountered in 219,985 and 168,265 plots corresponding to the 2012 and 2014 agricultural years with climate data. Also included in the analysis are the expected output and input prices, soil types, indicators of access to markets and information, socio-demographic characteristics of the farmer, and subsidy payments. We find strong evidence about the inappropriateness of the Independence of Irrelevant Alternatives (IIA) assumption underpinning the MNL model. This finding leads to remarkable differences in the predictions from the MNL and NL models. Speculations about the effect of climate change on farmers choices suggest that in the event of a warmer and drier future, Mexican agriculturalists will move their production efforts from alfalfa, cacao, beef cattle, grapes, onions, oranges, red tomato, soy, and sugar cane to bananas, barley, lemon, squash and potatoes. Acknowledgement :

Sensitivity evaluation of machine learning-based calibrated transportation mode choice models: A case study of Alexandria City, Egypt

The random coefficients logit model is identified