Parallel inverse aggregate demand curves in discrete choice models

Direct network effects, small-world networks, and industry formation

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

Cournot competition in wholesale electricity markets: The Nordic power exchange, Nord Pool

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.

This note establishes a new identification result for additive random utility discrete choice models. A decision-maker associates a random utility \(U_{j}+m_{j}\) to each alternative in a finite set \(j\in \left\{ 1,\ldots ,J\right\} \), where \(\mathbf {U}=\left\{ U_{1},\ldots ,U_{J}\right\} \) is unobserved by the researcher and random with an unknown joint distribution, while the perturbation \(\mathbf {m}=\left( m_{1},\ldots ,m_{J}\right) \) is observed. The decision-maker chooses the alternative that yields the maximum random utility, which leads to a choice probability system \(\mathbf { m\rightarrow }\left( \Pr \left( 1|\mathbf {m}\right) ,\ldots ,\Pr \left( J| \mathbf {m}\right) \right) \). Previous research has shown that the choice probability system is identified from the observation of the relationship \( \mathbf {m}\rightarrow \Pr \left( 1|\mathbf {m}\right) \). We show that the complete choice probability system is identified from observation of a relationship \(\mathbf {m}\rightarrow \sum _{j=1}^{s}\Pr \left( j|\mathbf {m} \right) \), for any \(s<J\). That is, it is sufficient to observe the aggregate probability of a group of alternatives as it depends on \(\mathbf {m}\). This is relevant for applications where choices are observed aggregated into groups while prices and attributes vary at the level of individual alternatives.

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.

Inverse demand and anti-giffen goods

Models of Count with Endogenous Choices

Models of count with endogenous choices

Assisted specification of discrete choice models

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

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

In this paper, we survey some aspects of the relationship between random utility, extreme value theory and multinomial logit models. In particular, we study the robustness of the assumption of a Gumbel distributed random utility. These ideas are well known within the field of spatial economics, but do not appear to be common knowledge to researchers in probability theory. The purpose of this paper is to try to bridge this gap.

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.