In economics, discrete choice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives, such as entering or not entering the labor market, or choosing between modes of transport. Such choices contrast with standard consumption models in which the quantity of each good consumed is assumed to be a continuous variable. In the continuous case, calculus methods (e.g. first-order conditions) can be used to determine the optimum amount chosen, and demand can be modeled empirically using regression analysis. On the other hand, discrete choice analysis examines situations in which the potential outcomes are discrete, such that the optimum is not characterized by standard first-order conditions. Thus, instead of examining "how much" as in problems with continuous choice variables, discrete choice analysis examines "which one". However, discrete choice analysis can also be used to examine the chosen quantity when only a few distinct quantities must be chosen from, such as the number of vehicles a household chooses to own [1] and the number of minutes of telecommunications service a customer decides to purchase.[2] Techniques such as logistic regression and probit regression can be used for empirical analysis of discrete choice.
Discrete choice models theoretically or empirically model choices made by people among a finite set of alternatives. The models have been used to examine, e.g., the choice of which car to buy,[1][3] where to go to college,[4] which mode of transport (car, bus, rail) to take to work[5] among numerous other applications. Discrete choice models are also used to examine choices by organizations, such as firms or government agencies. In the discussion below, the decision-making unit is assumed to be a person, though the concepts are applicable more generally. Daniel McFadden won the Nobel prize in 2000 for his pioneering work in developing the theoretical basis for discrete choice.
Discrete choice models statistically relate the choice made by each person to the attributes of the person and the attributes of the alternatives available to the person. For example, the choice of which car a person buys is statistically related to the person's income and age as well as to price, fuel efficiency, size, and other attributes of each available car. The models estimate the probability that a person chooses a particular alternative. The models are often used to forecast how people's choices will change under changes in demographics and/or attributes of the alternatives.
Discrete choice models specify the probability that an individual chooses an option among a set of alternatives. The probabilistic description of discrete choice behavior is used not to reflect individual behavior that is viewed as intrinsically probabilistic. Rather, it is the lack of information that leads us to describe choice in a probabilistic fashion. In practice, we cannot know all factors affecting individual choice decisions as their determinants are partially observed or imperfectly measured. Therefore, discrete choice models rely on stochastic assumptions and specifications to account for unobserved factors related to a) choice alternatives, b) taste variation over people (interpersonal heterogeneity) and over time (intra-individual choice dynamics), and c) heterogeneous choice sets. The different formulations have been summarized and classified into groups of models.[6] When discrete choice model are combined with structural equation models to integrate psychological (latent) variables, they are referred as hybrid choice models.[7]
^ abTrain, K. (1986). Qualitative Choice Analysis: Theory, Econometrics, and an Application to Automobile Demand. MIT Press. ISBN 9780262200554. Chapter 8.
^Train, K.; McFadden, D.; Ben-Akiva, M. (1987). "The Demand for Local Telephone Service: A Fully Discrete Model of Residential Call Patterns and Service Choice". RAND Journal of Economics. 18 (1): 109–123. doi:10.2307/2555538. JSTOR 2555538.
^Train, K.; Winston, C. (2007). "Vehicle Choice Behavior and the Declining Market Share of US Automakers". International Economic Review. 48 (4): 1469–1496. doi:10.1111/j.1468-2354.2007.00471.x. S2CID 13085087.
^Fuller, W. C.; Manski, C.; Wise, D. (1982). "New Evidence on the Economic Determinants of Post-secondary Schooling Choices". Journal of Human Resources. 17 (4): 477–498. doi:10.2307/145612. JSTOR 145612.
^Train, K. (1978). "A Validation Test of a Disaggregate Mode Choice Model" (PDF). Transportation Research. 12 (3): 167–174. doi:10.1016/0041-1647(78)90120-x. Archived from the original (PDF) on 2010-06-22. Retrieved 2009-02-16.
^Baltas, George; Doyle, Peter (2001). "Random utility models in marketing research: a survey". Journal of Business Research. 51 (2): 115–125. doi:10.1016/S0148-2963(99)00058-2.
In economics, discretechoice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives,...
in a particular context or contexts. Typically, it attempts to use discretechoices (A over B; B over A, B & C) in order to infer positions of the items...
Dynamic discretechoice (DDC) models, also known as discretechoice models of dynamic programming, model an agent's choices over discrete options that...
variables are quantitative, economic models are classified as discrete or continuous choice model; according to the model's intended purpose/function, it...
pioneered an approach that used only a choice task which became the basis of choice-based conjoint analysis and discretechoice analysis. This stated preference...
between continuous variables and discrete variables. (Discrete variables referring to more than two possible choices are typically coded using dummy variables...
higher education, structural estimation of dynamic discretechoice models, and college major choice, having written survey papers on each topic. He has...
dynamic discretechoice Models that simulate an agent's choices over discrete options that have future implications. Rather than assuming observed choices are...
unobservable factors. Traditional choice models, such as discretechoice models, rely solely on observable variables and choices made by individuals to infer...
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection...
observation i to category k. In discretechoice theory, where observations represent people and outcomes represent choices, the score is considered the utility...
trip making, while a discretechoice approach brings those variables inside the utility or impedance function. Discretechoice models require more information...
regression models are essentially the same as binary choice models, one type of discretechoice model: the primary difference is in the theoretical motivation...
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...
Mixed logit is a fully general statistical model for examining discretechoices. It overcomes three important limitations of the standard logit model by...
Nathan (2005). Loss Functions for Preference Levels: Regression with Discrete Ordered Labels (PDF). Proc. IJCAI Multidisciplinary Workshop on Advances...
implementation is easier. Sigmoid function, inverse of the logit function Discretechoice on binary logit, multinomial logit, conditional logit, nested logit...
prize was "for his development of theory and methods for analyzing discretechoice". He is the Presidential Professor of Health Economics at the University...
latent variable formulation of the multinomial logit model — common in discretechoice theory — the errors of the latent variables follow a Gumbel distribution...
{T}}A+\Gamma ^{\mathsf {T}}\Gamma .} Typically discrete linear ill-conditioned problems result from discretization of integral equations, and one can formulate...
Léopold; Zelenyuk, Valentin (2017). "Nonparametric estimation of dynamic discretechoice models for time series data" (PDF). Computational Statistics & Data...
linear model Generalized linear model Vector generalized linear model Discretechoice Binomial regression Binary regression Logistic regression Multinomial...
one of the founding fathers of the structural estimation of dynamic discretechoice models and the developer of the nested fixed point (NFXP) maximum likelihood...
linear model Generalized linear model Vector generalized linear model Discretechoice Binomial regression Binary regression Logistic regression Multinomial...
linear model Generalized linear model Vector generalized linear model Discretechoice Binomial regression Binary regression Logistic regression Multinomial...
University of Hong Kong, Shenzhen. Gallego is most known for his works on discretechoice models, dynamic pricing, pricing analytics, assortment optimization...
transformation may distribute the errors in a Gaussian fashion, so the choice to perform a nonlinear transformation must be informed by modeling considerations...
linear model Generalized linear model Vector generalized linear model Discretechoice Binomial regression Binary regression Logistic regression Multinomial...
DiscretechoiceDiscretechoice analysis Discrete distribution – redirects to section of Probability distribution Discrete frequency domain Discrete phase-type...
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