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, DK2800 Kgs. Lyngby, Denmark)

Institution 
Technical University of Denmark, DTU, DK2800 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 

Admin 
Creation date: 20090514
Update date: 20091104
Source: dtu
ID: 242848
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