Estimation Of Discrete Choice Models Research Articles

Identification and Estimation of Discrete Choice Models with Unobserved Choice Sets

We propose a framework for nonparametric identification and estimation of discrete choice models with unobserved choice sets. We recover the joint distribution of choice sets and preferences from a cross-section of repeated choices. We assume that either the latent choice sets are sparse or that the number of repeated choices is sufficiently large. Sparsity requires the number of possible choice sets to be relatively small. It is satisfied, for instance, when the choice sets are nested or when they form a partition. Our estimation procedure is computationally fast and uses mixed-integer programming to recover the sparse support of choice sets. Analyzing the ready-to-eat cereal industry using a household scanner dataset, we find that ignoring the unobservability of choice sets can lead to incorrect estimates of preferences.

Resampling estimation of discrete choice models

In the context of discrete choice modeling, the extraction of potential behavioral insights from large datasets is often limited by the poor scalability of maximum likelihood estimation. This paper proposes a simple and fast dataset-reduction method that is specifically designed to preserve the richness of observations originally present in a dataset, while reducing the computational complexity of the estimation process. Our approach, called LSH-DR, leverages locality-sensitive hashing to create homogeneous clusters, from which representative observations are then sampled and weighted. We demonstrate the efficacy of our approach by applying it on a real-world mode choice dataset: the obtained results show that the samples generated by LSH-DR allow for substantial savings in estimation time while preserving estimation efficiency at little cost.

Maximizing non-aeronautical revenues in airport terminals using gate assignment and passenger behaviour modelling

Airports must ensure that their operations can efficiently adapt to the emerging needs considering both the passenger experience and their economic viability. One way to achieve this is by optimizing the airport operations, aiming to maximize revenue levels considering operational objectives and passenger requirements inside the airport. This study presents an original mixed-integer linear programming model (MILP), which combines the gate assignment problem with passenger behaviour modelling. First, a survey was conducted to collect relevant information to model passenger behaviour and the purchases conducted in a terminal, leading to the estimation of discrete choice models that quantify the probability that a passenger makes purchases of certain levels at the terminal according to their flight type (departure, arrival or transfer). Then, the proposed MILP model assigns gates which would expectedly increase the airport non-aeronautical revenues at the terminal airport by matching flights and passenger gate categories to the most profitable gates, considering the proximity to the retail area, the walking distance needed to get to a gate in a specified time-horizon and the operational constraints of the airport. The application to the Lisbon Airport case study showed a potential increase of 8%–12.2% in revenues corresponding to 1732.7€ and 2967.3€ in half-an-hour time slots.

Can decision field theory enhance our understanding of health-based choices? Evidence from risky health behaviors.

Discrete choice models are almost exclusively estimated assuming random utility maximization (RUM) is the decision rule applied by individuals. Recent studies indicate alternative behavioral assumptions may be more appropriate in health. Decision field theory (DFT) is a psychological theory of decision-making, which has shown promise in transport research. This study introduces DFT to health economics, empirically comparing it to RUM and random regret minimization (RRM) in risky health settings, namely tobacco and vaccine choices. Model fit, parameter ratios, choice shares, and elasticities are compared between RUM, RRM and DFT. Test statistics for model differences are derived using bootstrap methods. Decision rule heterogeneity is investigated using latent class models, including novel latent class DFT models. Tobacco and vaccine choice data are better explained with DFT than with RUM or RRM. Parameter ratios, choice shares and elasticities differ significantly between models. Mixed results are found for the presence of decision rule heterogeneity. We conclude that DFT shows promise as a behavioral assumption that underpins the estimation of discrete choice models in health economics. The significant differences demonstrate that care should be taken when choosing a decision rule, but further evidence is needed for generalizability beyond risky health choices.

Bayesian estimation of discrete choice models: a comparative analysis using effective sample size

ABSTRACT In this paper, we provide a comparison of implementations of Bayesian estimation of mixed multinomial logit (MMNL) models. Our objective is to provide a systematic comparison of the runtime, efficiency, and model implementation details associated with several alternative workflows. The analysis is based on three case studies. We argue that previous comparisons in the transportation literature have lacked appropriate metrics for comparison. Effective sample size statistics are proposed as a means of accurately comparing the ability of Bayesian samplers to generate independent draws for use in statistical inference. The Allenby-Train algorithm implemented in the R package Apollo is compared with the NUTS sampler implemented in Stan. While the Allenby-Train algorithm tends to generate draws much faster than NUTS, we find that the high correlation between success samples makes the two methods comparable. In addition to traditional MCMC sampling, we also examine the method of variational Bayes (VB).

Identification and Estimation of Discrete Choice Models with Unobserved Choice Sets

We propose a framework for nonparametric identification and estimation of discrete choice models with unobserved choice sets. We recover the joint distribution of choice sets and preferences from a panel dataset on choices. We assume that either the latent choice sets are sparse or that the panel is sufficiently long. Sparsity requires the number of possible choice sets to be relatively small. It is satisfied, for instance, when the choice sets are nested, or when they form a partition. Our estimation procedure is computationally fast and uses mixed-integer optimization to recover the sparse support of choice sets. Analyzing the ready-to-eat cereal industry using a household scanner dataset, we find that ignoring the unobservability of choice sets can lead to biased estimates of preferences due to significant latent heterogeneity in choice sets.

Discrete Choice Model Estimation with Revealed Preference Data and Aggregate Service Level Variables

Discrete Choice Model Estimation with Revealed Preference Data and Aggregate Service Level Variables

Estimation of discrete choice models with hybrid stochastic adaptive batch size algorithms

The emergence of Big Data has enabled new research perspectives in the discrete choice community. While the techniques to estimate Machine Learning models on a massive amount of data are well established, these have not yet been fully explored for the estimation of statistical Discrete Choice Models based on the random utility framework. In this article, we provide new ways of dealing with large datasets in the context of Discrete Choice Models. We achieve this by proposing new efficient stochastic optimization algorithms and extensively testing them alongside existing approaches. We develop these algorithms based on three main contributions: the use of a stochastic Hessian, the modification of the batch size, and a change of optimization algorithm depending on the batch size. A comprehensive experimental comparison of fifteen optimization algorithms is conducted across ten benchmark Discrete Choice Model cases. The results indicate that the HAMABS algorithm, a hybrid adaptive batch size stochastic method, is the best performing algorithm across the optimization benchmarks. This algorithm speeds up the optimization time by a factor of 23 on the largest model compared to existing algorithms used in practice. The integration of the new algorithms in Discrete Choice Models estimation software will significantly reduce the time required for model estimation and therefore enable researchers and practitioners to explore new approaches for the specification of choice models.

A survey of preference estimation with unobserved choice set heterogeneity

We provide an introduction to the estimation of discrete choice models when choice sets are heterogeneous and unobserved to the econometrician. We survey the two most popular approaches: “integrating over” and “differencing out” unobserved choice sets. Inspired by Chamberlain (1980)’s original idea of constructing sufficient statistics from observed choices, we introduce the term “sufficient set” to refer to any combination of observed choices that lies within the true but unobserved choice set. The concept of sufficient set helps to unify notation and organize our thinking, to map econometric assumptions onto economic models, and to implement both methods in practice.

Semiparametric identification and estimation of discrete choice models for bundles

We study (point) identification of preference coefficients in semiparametric discrete choice models for bundles. The approach to the identification uses an “identification at infinity” (Chamberlain, 1986) insight in combination with median independence restrictions on unobservables. We propose two-stage maximum score (MS) estimators and show their consistency. Monte Carlo evidence demonstrates that our approach performs satisfactorily in finite samples.

Applying discrete choice models to understand sport tourists’ heterogeneous preferences for Winter Olympic travel products

This study aims to better understand how South Korean sport tourists show their preferences for Winter Olympic travel products. Comparing a series of discrete choice model (DCM) techniques, this study also investigates what attributes comprising PyeongChang Winter Olympic travel products are considered by sport tourists important and how they make trade-offs among those attributes for purchasing an optimal product. Study findings suggest that respondents place distinctive importance on each attribute to yield their greatest amount of utility through jointly considering a set of Olympic travel product attributes. Results also indicate that sport tourists put high willingness-to-pay values for multiple opportunities of attending skating competitions and popular tournaments while they show strong interests in more sightseeing and recreational experiences. Based on different DCM estimation results, several management strategies are presented for developing quality Olympic travel products.

Simulation error in maximum likelihood estimation of discrete choice models

Maximum simulated likelihood is the preferred estimator of most researchers who deal with discrete choice. It allows estimation of models such as mixed multinomial logit (MXL), generalized multinomial logit, or hybrid choice models, which have now become the state-of-practice in the microeconometric analysis of discrete choice data. All these models require simulation-based solving of multidimensional integrals, which can lead to several numerical problems. In this study, we focus on one of these problems – utilizing from 100 to 1,000,000 draws, we investigate the extent of the simulation bias resulting from using several different types of draws: (1) pseudo random numbers, (2) modified Latin hypercube sampling, (3) randomized scrambled Halton sequence, and (4) randomized scrambled Sobol sequence. Each estimation is repeated up to 1 000 times. The simulations use several artificial datasets based on an MXL data generating process with different numbers of individuals (400, 800, 1 200), different numbers of choice tasks per respondent (4, 8, 12), different number of attributes (5, 10), and different experimental designs (D-optimal, D-efficient for the MNL and D-efficient for the MXL model). Our large-scale simulation study allows for comparisons and drawing conclusions with respect to (1) how efficient different types of quasi Monte Carlo simulation methods are and (2) how many draws one should use to make sure the results are of “satisfying” quality – under different experimental conditions. Our study is the first to date to offer such a comprehensive comparison. Overall, we find that the number of the best-performing Sobol draws required for the desired precision exceeds 2 000 in some of the 5-attribute settings, and 20,000 in the case of some 10-attribute settings considered.

A body of knowledge representation model of ecotourism products in southeastern Ecuador

The corpus of knowledge or Bodies of Knowledge (BOK) term it used to describe a set of structures than codify all concept, terms, techniques, and sustainable activities that constitute the domain of the exercise of a profession or specific area of knowledge in our case in Ecotourism context. Ecotourism combines passion for travel with the interest in the preservation of nature and it is related to concepts of sustainability, conservation and participation of the local community, this term has been used to promote tourism activities in the natural environment and attract tourists interested in nature and culture of places to visit. In the Amazon rainforest ecotourism is an activity that contributes both to the awareness of travelers and the communities, in addition to income generated by this activity helps to preserve this heritage. The aim of this article is to contribute to the estimation of discrete choice models in order to analyze individual preferences, by analyzing the demand for ecotourism products in Ecuador's southeastern region, province of Zamora Chinchipe, using data obtained from surveys conducted during 2018, which provide information about the preferences of visitors to the area, through discrete choice experiments, and supported on BOK model. This experiment consisted in the creation of twelve choice scenarios defined by two hypothetical ecotourism products each. Thus, the alternatives were defined in terms of the following attributes: price, hiking, participation in rituals, tasting local cuisine, visit to crafts center and experience of community life (codes of BOK).

Efficiency Gains in Rank‐ordered Multinomial Logit Models

AbstractThis paper considers estimation of discrete choice models when agents report their ranking of the alternatives (or some of them) rather than just the utility maximizing alternative. We investigate the parametric conditional rank‐ordered Logit model. We show that conditions for identification do not change even if we observe ranking. Moreover, we fill a gap in the literature and show analytically and by Monte Carlo simulations that efficiency increases as we use additional information on the ranking.

An airline itinerary choice model that includes the option to delay the decision

Choice situations with variable supply characteristics are found in many applications, including airline itinerary selection. This paper discusses the airline itinerary choice problem in dynamic supply settings. The paper develops a specially designed stated preference (SP) survey, which emulates an air travel website. The survey includes the option to delay the decision to choose an airline itinerary. The rich data set allows the estimation of discrete choice models of airline itinerary choice.The paper presents selected model estimation and application results for two market sectors (tourists and business travelers) and two flight types (medium-haul and long-haul flights). In addition to expected results for several level-of-service variables such as flight cost, cancellation fees, connection times and punctuality percentages, the model estimates the expected value of delaying a flight purchase.

Applied Choice Analysis, 2nd edn, by David AHensher, John MRose and William HGreene. Published by Cambridge University Press, Cambridge, UK, 2015, pp. 1188, ISBN: 9781107092648 (Hardback), 9781107465923 (Paperback), AUD$155 (Paperback)

As a newcomer to the world of choice modelling, I sometimes get lost in the complicated world between economic choice theory, econometrics and statistics. Applied Choice Analysis Second Edition is a light to help you find your way. Though the reading itself is certainly not ‘light’, it is a substantially sized reference book that accidently ended up as an epic stand for my computer screen. However, it was quickly upgraded to prime position as a key reference because it provides a clear and comprehensive coverage of the theory and econometrics of choice modelling. This book is of interest both to the novice choice modeller and to the more experienced practitioner. The authors are prominent choice analysts and have developed this reference book while teaching graduate courses – and it shows. They explain all things choice modelling, without unnecessary technical language or jargon. This second edition was written in response to feedback on their first edition Applied Choice Analysis A primer and includes advances made since writing the first edition in 2004. The authors added numerous new sections, including generalised mixed logit, latent class analysis and a whole new chapter on more advanced topics. I notice that this Second Edition has a more relaxed conversational writing style (which is impressive given the technical nature of the content) and uses more examples to demonstrate theory and techniques. I also prefer the new formatting to increase readability and I particularly appreciate the overhanging chapter titles that makes finding sections easier. The book is generally structured by first introducing the relevant theory and concepts followed by using Nlogit as the software to demonstrate applications of the theory. The book is presented in three parts. Part I ‘Getting started’ covers topics in choice and utility, types and estimation of discrete choice models, experimental design and statistical inference. This first part provides 384 pages of choice modelling theory for your enjoyment, providing extensive background reading for any beginner or essential reference material for experienced practitioners. Towards the end of this section, there is an historical overview of the evolution of experimental design theory which more experienced users may find interesting. The next shorter section, Part II ‘Software and data’, moves into the more technical side of data analysis using the software Nlogit. This section introduces Nlogit and the software language and details the data set-up requirements for analysing discrete choice data sets in Nlogit. Part III ‘The suite of choice models’ is described by the authors as a ‘journey’, beginning with the multinominal logit model (the ‘workhorse’ of the choice modeller) through to more complex model specifications, such as nested, mixed and latent class logit models. This third part may be challenging for the novice reader, but essential material if you want to learn about the variety in choice models that is (or has been) used in the literature. The final Part IV ‘Advanced Topics’ is a new section that highlights some of the recent advancements to choice modelling, covering nonlinearity in parameter estimates, process heuristics and group decision-making. If you were lost in Part III, then you may need rescuing now. However, this is an interesting and important additional chapter as it begins to detail the frontiers of choice modelling and will be particularly useful for more advanced researchers and practitioners. The authors claim that this book is usable for the beginner, as I consider myself to be. Evidently, the authors assume you might be a beginner to choice modelling and not to econometrics or statistics, as for this second edition they have removed the introductory chapter on the Basic notions of statistics. This may not be a problem for most users who will have some background. Furthermore, the authors make every effort to bring you along regardless of your level by explaining concepts from the beginning, using examples and clear accessible language. While extremely useful for most choice modellers, the close integration with Nlogit software language and examples may provide some frustrations for practitioners who prefer different software. For example, preparing raw choice data for analysis can be a serious source of confusion. This book provides specific guidance for setting up data for use in Nlogit, which may be incomplete for researchers who are using other software. Despite the fact that I use different software, I find myself referring to this key reference book regularly on all topics from utility theory to complex model specifications, and I should probably refer to it more often. Finally, on the days when I cannot face any equations, I still find this text surprisingly readable and useful. I recommend this book to anyone, either beginning their choice modelling journey or looking to deepen their knowledge.

Duality in Dynamic Discrete Choice Models

Using results from Convex Analysis, we investigate a novel approach to identification and estimation of discrete-choice models that we call the mass transport approach. We show that the conditional choice probabilities and the choice-specific payoffs in these models are related in the sense of conjugate duality, and that the identification problem is a mass transport problem. Based on this, we propose a new two-step estimator for these models; interestingly, the first step of our estimator involves solving a linear program that is identical to the classic assignment (two-sided matching) game of Shapley and Shubik (1971). The application of convex-analytic tools to dynamic discrete-choice models and the connection with two-sided matching models is new in the literature. Monte Carlo results demonstrate the good performance of this estimator, and we provide an empirical application based on Rust's (1987) bus engine replacement model.

Duality in dynamic discrete-choice models

Using results from convex analysis, we investigate a novel approach to identification and estimation of discrete choice models which we call the Mass Transport Approach (MTA). We show that the conditional choice probabilities and the choice-specific payoffs in these models are related in the sense of conjugate duality, and that the identification problem is a mass transport problem. Based on this, we propose a new two-step estimator for these models; interestingly, the first step of our estimator involves solving a linear program which is identical to the classic assignment (two-sided matching) game of Shapley and Shubik (1971). The application of convex-analytic tools to dynamic discrete choice models, and the connection with two-sided matching models, is new in the literature.

The impact of education on intergenerational occupational mobility in Spain

Intergenerational occupational mobility is a topic that has attracted considerable interest in the sociological and economic literature for developed countries. In particular, one of the central issues in political debate is the role of education on the intergenerational social mobility. The modern capitalist economies are characterised by continual technological changes which lead to the need of a highly skilled workforce. In this potentially meritocratic society, the equality of opportunities, the efficient allocation of talent and the education can be instruments that encourage the social mobility and decrease the effect of the parents' economic status on the career of their children. This paper takes into account these facts and sheds empirical evidence for Spain about the relationships between social origin, educational attainment and occupational destination. The methodology applied consists of the specification and estimation of discrete choice models, and the empirical analysis is based on data provided by the Living Condition Survey (LCS) conducted for the Spanish National Statistics Institute (INE).

Accounting for stochastic variables in discrete choice models

The estimation of discrete choice models requires measuring the attributes describing the alternatives within each individual’s choice set. Even though some attributes are intrinsically stochastic (e.g. travel times) or are subject to non-negligible measurement errors (e.g. waiting times), they are usually assumed fixed and deterministic. Indeed, even an accurate measurement can be biased as it might differ from the original (experienced) value perceived by the individual.Experimental evidence suggests that discrepancies between the values measured by the modeller and experienced by the individuals can lead to incorrect parameter estimates. On the other hand, there is an important trade-off between data quality and collection costs. This paper explores the inclusion of stochastic variables in discrete choice models through an econometric analysis that allows identifying the most suitable specifications. Various model specifications were experimentally tested using synthetic data; comparisons included tests for unbiased parameter estimation and computation of marginal rates of substitution. Model specifications were also tested using a real case databank featuring two travel time measurements, associated with different levels of accuracy.Results show that in most cases an error components model can effectively deal with stochastic variables. A random coefficients model can only effectively deal with stochastic variables when their randomness is directly proportional to the value of the attribute. Another interesting result is the presence of confounding effects that are very difficult, if not impossible, to isolate when more flexible models are used to capture stochastic variations. Due the presence of confounding effects when estimating flexible models, the estimated parameters should be carefully analysed to avoid misinterpretations. Also, as in previous misspecification tests reported in the literature, the Multinomial Logit model proves to be quite robust for estimating marginal rates of substitution, especially when models are estimated with large samples.