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

Pr(i,j)=Pij =Pr(Uij ≥Uik)
=Pr(εik -εij ≤Vij -Vik)
= F (Vj- Vik )= F W (X ’,«)]

where F represents the distributive function of (εik - εij) and H represents the functional
form of the relation (V_ij -V_ik). H is lineal one. In a binarial case with transport alternatives 1
and 2 are expressed like:

U_i1 = X_iβ₁ + Z _i1α+ ε_i1

U_i2 = X_iβ₂ + Z_i2α+ε_i2

where Xi are the variables that correspond to the individual caracteristics and Zij are the
attributes of the considered alternatives.

The individual i chooses the alternative j (Yi = 1) if Uil > Ui2 it means,

Y_i = 1 si X _i ^, β+(Z_i1 - Z_i2 )α+ ε_i > 0

Y_i = 0 on the contrary
whereβ=(β₁ -β₂)y ε_i = (ε_i1 -ε_i2)

According to this planning, the choice of a decided alternative according to the attributes
associated to each one of them (Zij) does not depends on their absolute values but on their
differences.

An economical model of discrete choice means the necesity to choose a distribution of
probability of the model (F). When the individual faces to binary alternatives, the most
usual functions are the ones that give place to logit and probit models, in this case the
chosen model is binomial probit that is based on the supposition that the function F is
distributed according to a rule, being the probability of choosing the alternative 1:

P (γi = 1)= φ(X * 'r)

<<   1   2   3   4   5   6   7   >>

More intriguing information