A comparison of two alternative behavioral choice mechanisms for household auto ownership decisions

Representation of heteroskedasticity in discrete choice models

Choice models are used to explain and predict how consumers choose among multiple alternatives, usually brands within a product category (such as ketchup and laundry detergent). The most popular one is the multinomial logit (MNL) model, which has been used in numerous marketing research applications. The article starts with a discussion of the MNL, explicitly discussing least squares and maximum likelihood techniques that are used to calibrate the model, as well as hypothesis tests and measures of model fit. The IIA problem associated with the MNL model is discussed. This leads to a discussion of the multinomial probit (MNP) model, the second most popularly used choice model in Marketing, which alleviates some of the concerns arising out of the IIA problem. Estimating the MNP model, which does not have an analytical closed form (as does the MNL), requires simulation methods. Two popularly used simulation techniques, the frequency‐based simulator and the smooth recursive conditioning (SRC) simulator, are discussed in detail. Lastly, the article briefly discusses some alternative choice models (generalized extreme value (GEV), nested logit, Batsell and Polking) that also relax the IIA restriction of the MNL model, while also yielding closed‐form choice probabilities.

Empirical studies on household car ownership have used two types of discrete choice modeling structures: ordered and unordered. In ordered response structures, such as the ordered logit and ordered probit models, the choice of the number of household vehicles arises from a unidimensional latent variable that reflects the propensity of a household to own vehicles. Unordered response structures are based on the random utility maximization principle, which assumes a household associates a utility value across different car ownership levels and chooses the one with the maximum utility. The most common unordered response models are the multinomial logit and probit models, but only the multinomial logit has been used in practical applications because of its simple structure and low computational requirements. Consensus among researchers on unordered or ordered structures is still lacking. Empirical studies have reported various models, including the multinomial logit, ordered logit, and ordered probit. An open question remains: Which model would better reflect households’ car ownership choices? This paper compares multinomial logit, ordered logit, and ordered probit car ownership models through a number of formal evaluation measures and empirical analysis of three data sets: the 2001 National Household Travel Survey for the Baltimore [Maryland] Metropolitan Area, the 2005 Dutch National Travel Survey, and the 2000 Osaka [Japan] Metropolitan Person Trip Data. Results show the multinomial logit model should be selected for modeling the level of household car ownership.

Better understanding of households’ fuel type choice behaviour for residential heating, cooking, or lighting purposes would provide valuable information in estimating households’ energy use and in developing efficient fuel switching and energy saving policies; these solutions could include reducing consumption and utilising renewable energy sources. This paper aims to explore potential determinants of household’s fuel choice for residential heating in Türkiye. Using nineteenth wave of Household Budget Survey which was administered to 11,828 households and 40,688 individuals throughout the country, the data were analysed using both multinomial logit (MNL) and multinomial probit (MNP) models due to unordered nature of the dependent variable category. The empirical findings indicate household type, type of dwelling, residence time, the age of dwelling, the number of rooms, housing size, household size, type of floor structure of dwelling, household annual disposable income (log), household head’s occupation level, type of heating system, car ownership, and type of employment were found as statistically significant factors affecting Turkish household’s fuel choice for residential heating. Household annual disposable income and type of heating system had the highest impact on household’s final fuel type decision. Results also reveal that MNL is more parsimonious model than MNP model.

مطالعه حاضر با هدف بررسی نحوه اثرگذاری متغیرهای آب و هوایی شامل دما، بارش، سرعت باد و رطوبت بر سهم سطح زیرکشت انواع محصولات سالانه زراعی شامل غلات، حبوبات، سبزیجات، محصولات جالیزی، محصولات علوفه ای و محصولات صنعتی در ایران صورت گرفت. در این راستا با استفاده از اطلاعات زراعی و هواشناسی 336 شهرستان کشور در دوره زمانی 92-1391 اقدام به برآورد مدل لاجیت چندگانه کسری گردید. نتایج مطالعه نشان داد افزایش دما سهم سطح زیرکشت غلات و محصولات جالیزی را افزایش و سهم سطح زیرکشت حبوبات را کاهش می-دهد. لذا با توجه به پیش بینی های صورت گرفته در مورد افزایش دما در سال های آتی، انتظار بر این است که میزان کشت غلات افزایش و میزان کشت حبوبات کاهش یابد. بارش متغیر دیگری است که با افزایش آن سهم سطح زیرکشت غلات افزایش و سهم سایر انواع محصولات کاهش می-یابد. درصد رطوبت بر سهم سطح زیرکشت سبزیجات و محصولات صنعتی و سرعت باد نیز بر سهم سطح زیرکشت محصولات صنعتی و غلات موثر می باشد. از این رو توصیه می گردد نحوه واکنش تولیدکنندگان محصولات زراعی سالانه به تغییرات آب و هوایی تحت سناریوهای گوناگون پیش بینی و با مقایسه مقدار تولید بالقوه با نیازهای غذایی جامعه در آینده و تعیین شکاف های موجود، مبنای سیاست گذاری های لازم در این زمینه فراهم شود. همچنین با توجه به اینکه مطالعه حاضر تنها تخصیص زمین بین انواع محصولات سالانه زراعی را مدنظر قرار داده است، توصیه می-گردد مطالعات دیگری نیز در زمینه بررسی نحوه اثرگذاری تغییرات آب و هوایی بر تولیدات سایر بخش های کشاورزی از قبیل محصولات باغی و دامی صورت گیرد.

The accuracy of the multinomial logit model as an approximation to the multinomial probit model of travel demand

Utility independence versus IIA property in independent probit models

This paper developed a mixed multinomial probit (MMNP) model with alternative error specification and random coefficients (for both generic variables and personal attributes) to accommodate flexible covariance structure and taste variation. The MMNP model can be efficiently estimated with analytic approximations of multivariate normal cumulative distribution functions, which avoid defects of simulation-based integration in the mixed multinomial logit (MMNL) model. The integral dimension of the MMNL model increases as random coefficients increase, but it only depends on the number of available alternatives in the MMNP model. Simulation experiments and empirical analysis of Shanghai commuters’ mode choice behavior were undertaken to examine the performance of MMNP models. Both simulation results and empirical results show that MMNP models can well accommodate flexible covariance structures and taste variation reflected through random coefficients being associated with both generic and personal variables. Empirical results indicate that the MMNP model performs better than traditional discrete choice models, such as the multinomial logit, the cross-nested logit, MMNL, and multinomial probit models. Random coefficients of “in-vehicle time of car” and “number of companions” indicate taste heterogeneity and the identifiability of random coefficients associated with both generic and personal attributes. Pairwise positive correlations between car/taxi, bus/metro, and bus/bus and metro are to be expected. However, the positive correlation between the car and metro modes may be unique to the Chinese city, Shanghai, because of the developed metro system. Unequal error variances reflect heterogeneities in unspecified factors in commute modes’ utilities. The MMNP model will offer an alternative efficient way to accommodate taste heterogeneity and flexible error covariance structure in discrete choice models. Compared with the MMNL model, the MMNP model can accommodate more random coefficients without increasing computational complexity.

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.

Freight vehicle crashes are more serious than regular vehicle crashes because they are likely to lead to major damage and injury once they occur; therefore, countermeasures are needed. The fatality rate from freight vehicle crashes is 1.5 times higher than that of all other accidents, and the death rate from expressway freight vehicle crashes continues to increase. In this study, the ten-freight-vehicle crash severity models (the ordered logit and probit model, the multinomial logit and probit model, mixed-effects logit and probit model, random-effects ordered logit and probit model, and multilevel mixed-effects ordered logit and probit model) are used to analyze the freight vehicle crash severity factors. The model was constructed using data collected from expressways over eight years, and 13 factors were derived to increase the severity of crashes and 7 factors to reduce the severity of crashes. As a result of comparing the 10 constructed models using AIC and BIC, the multilevel mixed-effects ordered probit model showed the best performance. It is expected that it can contribute to improving the safety of freight vehicles in the expressway section by utilizing factors related to the severity of crashes derived from this study.

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.

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.

Multinomial choice models are used for the analysis of unordered, mutually exclusive choice alternatives. Conventionally used multinomial choice models are the multinomial logit, nested logit, multinomial probit and random parameters logit models. This paper develops multinomial choice models based on Archimedean copulas. In contrast to the multinomial logit and nested logit models, no independence of irrelevant alternatives property is implied. Moreover, copula-based multinomial choice models are more parsimonious than the multinomial probit and random parameters logit models, which makes them attractive from a computational point of view and makes them particularly suitable for prediction purposes. When the number of alternatives becomes large, additional complexity can be introduced using nested Archimedean copulas. Nested structures can often be motivated from individual behavior. The paper also considers an empirical application to travel mode choice. It is found that copula-based multinomial choice models provide a good compromise between fit and parsimony.

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

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.