A note on identification in discrete choice models with partial observability

This paper analyzes and synthesizes the fundamentals of discrete choice models. This paper alsodiscusses the basic concept and theory underlying the econometrics of discrete choice, specific choicemodels, estimation method, model building and tests, and applications of discrete choice models. Thiswork highlights the relationship between economic theory and discrete choice models: how economictheory contributes to choice modeling and vice versa.
 Keywords: Discrete choice models; Random utility maximization; Decision makers; Utility function;Model formulation

This paper highlights a previously unnoticed property of commonly-used discrete choice models, which is that they feature parallel demand curves. Specifically, we show that in additive random utility models, inverse aggregate demand curves shift in parallel with respect to variety if and only if the random utility shocks follow the Gumbel (Type 1 Extreme Value) distribution. Using results from Extreme Value Theory, we provide conditions for other distributions to generate parallel demands asymptotically, as the number of varieties increases. We establish these results in the benchmark case of symmetric products, illustrate them using numerical simulations and show that they hold in extended versions of the model with correlated tastes and asymmetric products. Lastly, we provide a “proof of concept” of parallel demands as an economic tool by showing how to use parallel demands to identify the change in consumer surplus from an exogenous change in product variety.

Discrete choice models in economics are often used to mathematically model the heuristic approaches that people use in decision-making. When faced with a large number of choices, however, people face information costs that lead to choice overload. Within the discrete choice framework, here we formulate a quantization-theoretic approach to optimally cluster choices into categories. This is a non-asymptotic form of rational inattention theory. Drawing on a recent equivalence result between discrete choice models and Bregman divergences, and on properties of Bregman clustering, our main result is that the same clustering algorithm is universally optimal for any additive random utility discrete choice model. Examples are given and hierarchical clustering is also discussed.

Models of Count with Endogenous Choices

What is the Impact of Non-Randomness on Random Choice Models?

Models of count with endogenous choices

Discrete choice models are a group of models that are used to analyze choice data basically because they accommodate the nature of the process that generates the data. The most common types of discrete models include the logit, probit, multinomial logit, nested logit, mixed logit and most recently the generalized multinomial logit. Discrete choice models have been mostly used in the area economics, transportation, energy, psychology, etc. Prediction in these models isn\\'t uncommon, in contexts such as engineering, marketing, and production, discrete choice models are mostly used to forecast demand. Unfortunately, for out-of-sample prediction at the individual level for complex models such as mixed logit, which involves predicting the random effects/parameters, there isn\\'t any work found in literature. Thus, in this is work we propose a method for this scenario in mixed logit discrete models using the nearest neighbour concept. We carry out various simulations and then apply on two types of real-life data. We find that the prediction accuracy of this new method is better than the rudimentary method of using the population parameters especially when the model fitted isn\\'t the very best.

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.

The mHealth applications (mHealth apps) are shown as a promising and scalable solution for addressing various healthcare challenges and improving overall health outcomes. This study employs additive utility theory and random utility and discrete choice modeling to investigate the role of health literacy and the key constructs proposed in the Health Belief Model (HBM), namely perceived benefits, perceived barriers, perceived susceptibility, perceived severity, and self-efficacy, in influencing mHealth apps preferences. This study was conducted using a sample of 353 participants in Malaysia who are aged above 21 years old and have an income. Results show that Health Services Apps (English) is the most preferred by respondents, with education level as the strongest predictor of choice. Besides, English is the most preferred language in each category of mHealth apps as compared to the other languages. The results provide useful insights for policymakers and app developers to develop appropriate strategies for the integration of mHealth apps with existing healthcare systems. At the theoretical level, this study tries to expand the dimensions of additive utility theory on research of mHealth apps preferences and further enriches the application areas of HBM.

Marketing practitioners and academics have shown a keen interest in the processes that drive consumers’ choices since the early work of Guadagni and Little (1982). Over the past decade or so, a number of alternative models have been proposed, implemented and analyzed. The common behavioral assumption that underlines these models of discrete choice is random utility maximization (RUM). The RUM assumption, in its simplest form, posits that a consumer with a finite set of brands to choose from chooses the brand that gives her the maximum amount of utility. An alternative approach would be to assume that consumers choose the alternative that offers them the least disutility. Our paper proposes and tests a broad class of generalized extreme value models based on this hypothesis. We model the decision process of the consumer the assumption random disutility minimization (RDM) and derive a new class of discrete choice models based on this assumption. Our findings reveal that there are significant theoretical and econometric differences between the discrete choice models derived from a RUM framework and the RDM framework proposed in this paper. On the theoretical front we find that the class of discrete choice models based on the assumption of disutility minimization is structurally different from the models in the literature. Further, the models in this class are available in closed form and exhibit the same flexibility as the GEV models proposed by McFadden (1978). In fact, the number of parameters are identical to and have the same interpretation as those obtained via RUM based GEV models. In addition to the theoretical differences we also uncover significant empirical insights. With the computing effort and time for both models being roughly the same this new set of models offers marketing academics and researchers a viable new tool with which to investigate discrete choice behavior.

This paper develops nonparametric estimation for discrete choice models based on the mixed multinomial logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random utility maximization, subject to the identification of an unknown distribution $G$. Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution $G$, to estimate choice probabilities. We provide an important theoretical support for the use of the proposed methodology by investigating consistency of the posterior distribution for a general nonparametric prior on the mixing distribution. Consistency is defined according to an $L_1$-type distance on the space of choice probabilities and is achieved by extending to a regression model framework a recent approach to strong consistency based on the summability of square roots of prior probabilities. Moving to estimation, slightly different techniques for non-panel and panel data models are discussed. For practical implementation, we describe efficient and relatively easy-to-use blocked Gibbs sampling procedures. These procedures are based on approximations of the random probability measure by classes of finite stick-breaking processes. A simulation study is also performed to investigate the performance of the proposed methods.

Discrete choice model is probably one of the most popularly used statistical methods in practice. The common feature of this model is that it considers the behavioral factors of a person and the assumption of independent individuals. However, this widely accepted assumption seems problematic because human beings do not live in isolation. They interact with each other and form complex networks. Then the application of discrete choice model to network data will allow for network dependence in a general framework. In this paper, we focus on a discrete choice model with probit error which is specified as a latent spatial autoregressive model (SAR). This model could be viewed as a natural extension of the classical SAR model. The key difference is that the network dependence is latent and unobservable. Instead, it could be measured by a binary response variable. Parameter estimation then becomes a challenging task due to the complicated objective function. Following the idea of composite likelihood, an approximated paired maximum likelihood estimator (APMLE) is developed. Numerical studies are carried out to assess the finite sample performance of the proposed estimator. Finally a real dataset of Sina Weibo is analyzed for illustration purpose.

On substitutability and complementarity in discrete choice models

A previously reported positive influence of a distractor alternative on decision accuracy was driven by an unintended covariation between key variables, beyond which the distractor has a modest negative influence on accuracy, possibly mirroring asymmetric multiattribute context effects.

It is often the case that a discrete choice model cannot be applied to forecasting because the choice set is unmanageably large and choice probabilities cannot be evaluated in a practical manner. For example, an activity-based analysis of travel behavior often involves an astronomical number of potential activity travel patterns, resulting in an enormous choice set when one attempts to formulate the behavior as a discrete choice. A colossal choice set makes it practically impossible to define the full choice set and to evaluate the choice probability of each pattern for forecasting. An algorithm is presented for the simulation of individuals’ activity travel choice by sampling activity travel patterns from a colossal choice set, according to their choice probabilities as determined by a discrete choice model without enumeration of the full choice set. Numerical examples demonstrate the practicality and effectiveness of the algorithm in forecasting the effects on activity travel patterns of transportation policy measures.