Page 382 - 360.revista de Alta Velocidad - Nº 5

Pagliara, Francesca. Menicocci, Fabrizio.Vassallo, José Manuel. Gómez Sánchez, Juan.

where:

β is the intercept, i.e. the expected value of p when all the predictors are 0;
0
β i are the regression coefficients, estimated through the calibration process.

As a consequence of this linearization process, the interpretation of the β coefficients is
k
different compared to standard linear regression models. The slope coefficient suggests that
for a unit increase in a certain explanatory variable X , the weighted log of the odds in favor of
k
βk
a certain alternative (Y=1) increases of e . Moreover, for a unit increase of a given explanatory
βk
variable X , the odds ratio in favor of happening Y=1 increases of e . Furthermore, unlike a
k
simple linear regression, logistic regression parameters are usually estimated with the method
of maximum likelihood, an iterative process calculating small corrections until the convergence
is reached.
Regarding the goodness of fit of the model, R statistics refer to the entire model and indicates
2
how useful the explanatory variables are in predicting the response variable. The Cox & Snell
and the Nagelkerke R are two of the most used statistics. The maximum value for Cox & Snell
2
2
2
R is less than 1 while the Nagelkerke R provides a correction of this one and covers the full
range from 0 to 1 and therefore is often preferred.
A preliminary analysis has been carried out to check potential collinearity between the
explanatory variables ECO-EXC and INCOME < 2000. Specifically a correlation analysis based on
the Chi2 test allows determining the level of relationship between both variables. With a level
of significance equal to 0.05 and 1 degree of freedom, according to the Chi test the alternative
2
hypothesis is accepted and the variables are independent. Estimation results for the binary
choice model specified are reported in Table 7. According to the estimates it can be observed
that:
• Those users who have travelled at least once by Spanish HSR (AVE) have a higher
probability of choosing it again (β positive and highly significant).
ALREADY-TRAV-HSR
• Those users who feel to be economically excluded (i.e. for whom the cost of the HSR
ticket is perceived high) have a lower probability of choosing HSR (β ECO-EXC negative and
significant).
• Those users who feel to be time-based excluded (i.e. who feel constrained due to the
impossibility of reconciling their commitments with train frequency and timetable) have a
low probability of choosing HSR (β TIME-EXC negative and highly significant), keeping the rest of
variables constant.
• Those users who feel to be geographically excluded (i.e. who have a lower accessibility
to AVE stations) have a low probability of choosing HSR (β negative and significant).
GEO- EXC
• Those users who have a monthly income under 2,000 Euro have a lower probability of
choosing AVE (β INCOME<2000 negative). Moreover this variable is not statistically significant
(t–ratio = 1.684 < 1.960).

Table 7 - Estimation results (not all the variables significant)

380 360.revista de alta velocidad