The demand for urban transport: An application of discrete choice model for Cadiz

2.- Discrete choice model: probit model.

Discrete choice model allows us to study the individuals behaviour when this has to face
discrete decisions like in this case, to choose between urban transport or private transport
(Gallastegui, 1985). These models esteem demand functions from individual facts what
allows us to foretell with more exactitude changes effects in the attributes of transport ways
(Gonzalez et al., 1995; Matas, 1991).

Qualitative answer models have been used in different areas of economical investigation
(Amemiya, 1981) being in the transport economy field Mac Fadden (1974, 1981) who from
a maximizing theory of the aleatory utility that means the existence of rational customers
and basing on a marginal micro-economical analysis, he formulated a discrete choice model
that makes possible the esteem of the function for demand of transport.

This methodology is based on the idea that each customer maximizes its utility according to
a group of continuous well-living Z and a group of discrete alternatives,j, joined to a
estimative restriction R. The maximization of the utility U(Z,j) means that first of all the
individual maximizes U(Z,j) according to the well-living Z for each alternative and then he
chooses the alternative j that maximizes the entire utility.

max{maxU (Z, j)s.r. pZ ≤ R}
jZ

The indirect function of utility is got of the first maximization, for an individual i and for
each alternative j we can represent it like:

Uj(χX )= Vj (X ')+ε₁

Where X* gathers the prices, the rent and the relevant attributes of the alternatives and
individuals Vij represents the common utility to all the individuals only in its structure
because X* is different depending on the alternatives and the individuals εij is an aleatory
variable with a function of given probability and being able to be interpreted like the effect
of the caracteristics of non-measurable pleasures of the individual.

The maximization of the utility about the alternatives means the that the individual i will
choose the alternative j if Uij >U_ik ∀ k ≠ j, and then.

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