Decision Models in Skiable Areas - EPFL

6 MODEL OF DEMAND IN A SKIABLE AREA 12
• Min has a negative sign. This is also interpretable, in the way that a low ”Min”
(MinLD = mins∈SL D ls) is more attractive.
• Prot has a positive sign and this means that a lift where the skiers are protected
against the weather is more attractive. We have seen that this attribute coincides
with the characteristic to put off the skis. This means that the protection against
the weather is more appreciated by the skiers than the disadvantage to put off the
skis.
• Seats has also a positive sign. A lift where the skiers can sit down is more
attractive than one without the possibility to sit down.
The sign of the coefficient Maxmax can not be interpreted, because the positive sign of
the attribute Max tells us that the skiers like the high-level ski slopes. So it could also
be suspected that the coefficient Maxmax has a positive sign. Or, at least that the both
coefficients have the same sign.
Because the two attributes Manmax D O and P rotD has to be supposed random
variables and because the sign of the coefficient Maxmax can not be interpreted, it is
likely that the Basic Model can be improved. The fact that the attributes Manmax D O
and P rotD are random variables leads to the first approach, the time dependence of
the coefficients Minmax and Prot. This is described in section 6.1.3. The fact, that the
sign of the coefficient Maxmax can not be interpreted in an intuitive way is, as already
mentioned, the motivation of the second approach in section 6.1.4.
6.1.3 First approach: Time dependence of ”Minmax” and ”Prot”
View that the coefficients ”Minmax” and ”Prot” are random variables, a time dependence
of this coefficients is proved. It is assumed that the coefficient in the deterministic
term corresponding to Minmax is
�
T ime
Minmax ·
t0
� λmo
∀ T ime < t0
where the time is measured in minutes and t0 chosen to be 720, what correspond to
noon (starting at midnight). In the afternoon, we have
�
T ime
Minmax ·
t0
� λan
∀ T ime ≥ t0
An example of this function depending of the time is illustrated in Figure 3 where
Minmax is set to 1, λmo and λan to -1.72 and 0.58 respectively. The parameters λmo
and λan can also be estimated by Biogeme. The same approach is done in the case of
the coefficient ”Prot”. This leads to two coefficients µmo and µan. All together, four
additional parameters has to be estimated in this model.
The result of this estimation is illustrated in Figure 4. It can be observed that µmo
is not significant and it reaches the lower bound of −5 which is very unrealistic. The
attribute σan is also not significant. The failure of the t-test means that the hypotheses
of time dependence of the two attributes has to be rejected. You can also remark that
the sign of Maxmax is still negative. This is the reason, why we leave the strategy to
ameliorate the attributes Minmax and Prot. We rather look to change the model that
Maxmax becomes a positive number (Or at least that Max and Maxmax have the same
sign).
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