## Beta 1

Title Extending the framework for MEV discrete choice models
Author Santini, Lorenza
Supervisor Fosgerau, Mogens (Transport Economics, Department of Transport, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2009
Abstract Discrete choice models are used to describe situations where an individual has a nite number (1; ;A) of alternatives to choose from. We suppose the individual to be rational in the sense that it will choose the alternative that maximizes his preferences: the alternative with the maximum utility function. The utility function is a function of the attributes of the alternative and it is composed by a deterministic part and by an error term that is a random variable. We are interested in nding the probability with which the individual chooses each alternative, that is equivalent in nding the probability that the utility of each alternative is bigger than all the other utilities, we need to know the distribution of the maximum of a nite number of random variables. The distribution of the maximum of a nite number of random variables belongs to the class of extreme value distributions, which comprises three dierent distributions, distinguished by a parameter that may be positive, negative or zero. The distribution with parameter zero, the Gumbel distribution, is the basis for an extremely popular class of statistical models, starting with the Multinomial Logit model to complex mixtures of Multivariate Extreme Value models. However, there are no discrete choice models based on the two other distributions: the Fréchet and the Weibull distributions. This is a restriction for the Multivariate Extreme Value models because we impose a distribution instead of deduce it from the data. We will then introduce the Multivariate Generalized Extreme Value (MGEV) model that generalizes the Multivariate Extreme Value class of models adding one new parameter to the choice probability. We will reformulate the utility function so that, estimating the new parameter from the data, it will be possible to select the distribution that best ts the data among the Gumbel, the Fréchet and the Weibull distributions. Then the choice of the distribution will depend on the value of the new parameter, which can be positive, 4 negative or zero. This new parameter increases the exibility of the model: the shape of the probability function that the model has to compute varies with the parameter and then the data can be better described. In this paper we will rst present some background review about the extreme value distributions and about the discrete choice models. Then we will derive and present the MGEV model giving the new utility function, computing the choice probability, analyzing the increase of the exibility and making the identication of the parameters that have to be estimated from the data. Hence we will make a simulation study to analyze the quality of the MGEV model.
Imprint Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Pages 85
Keywords Discrete choice modelas
Fulltext
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Admin Creation date: 2009-05-14    Update date: 2009-11-04    Source: dtu    ID: 242848    Original MXD