Discrete Choice Methods with Simulation. Kenneth Train Published by Cambridge University Press First edition, Second edition,
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- Discrete Choice Methods with Simulation
- Discrete Choice Methods with Simulation by Kenneth E. Train
- Discrete Choice Methods with Simulation (2002)
Train offers thoughtful insights on each of the major models: Train also investigates and compares a range of simulation-assisted estimation procedures that are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing. Covering a broad range of topics with great clarity and depth, this book is a must-read for advanced choice modelers -- and can even serve as a textbook for advanced students of discrete choice analysis.
What people are saying No other book covers this ground with such up-to-date detail in respect of theory and implementation. The chapters on simulation and recent developments such as mixed logit are most lucid. We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings. View all Google Scholar citations for this book. Email your librarian or administrator to recommend adding this book to your organisation's collection.
This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. This second edition adds chapters on endogeneity and expectation-maximization EM algorithms.
No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing. To send content items to your account, please confirm that you agree to abide by our usage policies.
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Get access Buy the print book. Check if you have access via personal or institutional login. Log in Register Recommend to librarian. The utility of each alternative depends on the attributes of the alternatives interacted perhaps with the attributes of the person. The unobserved terms are assumed to have an extreme value distribution. We can relate this specification to model A above, which is also binary logit.
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In particular, P n 1 can also be expressed as. Note that if two error terms are iid extreme value , [nb 1] their difference is distributed logistic , which is the basis for the equivalence of the two specifications. The description of the model is the same as model C , except the difference of the two unobserved terms are distributed standard normal instead of logistic. The utility for all alternatives depends on the same variables, s n , but the coefficients are different for different alternatives:.
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The utility for each alternative depends on attributes of that alternative, interacted perhaps with attributes of the person:. Note that model E can be expressed in the same form as model F by appropriate respecification of variables. Then, model F is obtained by using. A standard logit model is not always suitable, since it assumes that there is no correlation in unobserved factors over alternatives.
This lack of correlation translates into a particular pattern of substitution among alternatives that might not always be realistic in a given situation. This pattern of substitution is often called the Independence of Irrelevant Alternatives IIA property of standard logit models.
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The model is the same as model F except that the unobserved component of utility is correlated over alternatives rather than being independent over alternatives. The model is the same as model G except that the unobserved terms are distributed jointly normal , which allows any pattern of correlation and heteroscedasticity:. The integral for this choice probability does not have a closed form, and so the probability is approximated by quadrature or simulation. Mixed Logit models have become increasingly popular in recent years for several reasons. Second, the advent in simulation has made approximation of the model fairly easy.
In addition, McFadden and Train have shown that any true choice model can be approximated, to any degree of accuracy by a mixed logit with appropriate specification of explanatory variables and distribution of coefficients.
Discrete Choice Methods with Simulation
The integral for this choice probability does not have a closed form, so the probability is approximated by simulation. In many situations, a person's ranking of alternatives is observed, rather than just their chosen alternative. Or, in a survey, a respondent might be asked:. The models described above can be adapted to account for rankings beyond the first choice. The most prominent model for rankings data is the exploded logit and its mixed version. Under the same assumptions as for a standard logit model F , the probability for a ranking of the alternatives is a product of standard logits.
The model is called "exploded logit" because the choice situation that is usually represented as one logit formula for the chosen alternative is expanded "exploded" to have a separate logit formula for each ranked alternative. The exploded logit model is the product of standard logit models with the choice set decreasing as each alternative is ranked and leaves the set of available choices in the subsequent choice. Without loss of generality, the alternatives can be relabeled to represent the person's ranking, such that alternative 1 is the first choice, 2 the second choice, etc.
The choice probability of ranking J alternatives as 1, 2, …, J is then. As with standard logit, the exploded logit model assumes no correlation in unobserved factors over alternatives. The exploded logit can be generalized, in the same way as the standard logit is generalized, to accommodate correlations among alternatives and random taste variation.
Discrete Choice Methods with Simulation by Kenneth E. Train
The "mixed exploded logit" model is obtained by probability of the ranking, given above, for L ni in the mixed logit model model I. This model is also known in econometrics as the rank ordered logit model and it was introduced in that field by Beggs, Cardell and Hausman in A multinomial discrete-choice model can examine the responses to these questions model G , model H , model I. However, these models are derived under the concept that the respondent obtains some utility for each possible answer and gives the answer that provides the greatest utility.
It might be more natural to think that the respondent has some latent measure or index associated with the question and answers in response to how high this measure is.
Discrete Choice Methods with Simulation (2002)
Ordered logit and ordered probit models are derived under this concept. Assume that there are cutoffs of the level of the opinion in choosing particular response. For instance, in the example of the helping people facing foreclosure, the person chooses. When there are only two possible responses, the ordered logit is the same a binary logit model A , with one cut-off point normalized to zero.
The description of the model is the same as model K , except the unobserved terms have normal distribution instead of logistic.