*4.4. Validation*

The time parameter had a negative sign (present in the no alternative). In fact, as time increased there was a greater propensity to choose the MaaS alternative. The bundle cost parameter had a negative sign because the higher the bundle cost, the lower a user's propensity to purchase MaaS packages. The scenario parameter state had a positive sign because the utility increased with the number of subscenarios chosen. All the calibrated models were acceptable in terms of the signs of the parameters.

The VOT varied from a maximum of EUR 150 to a minimum of EUR 8 for scenario 1, from a maximum of EUR 218 to a minimum of EUR 6 for scenario 2, and from a maximum of EUR 105 to a minimum of EUR 8 for scenario 3. The best results were those characterized by a low VOT, consistent with the users surveyed who traveled for work, study, or other reasons, such as errands or leisure. The best calibrated models in term of VOT were III and IV.

The Student's *t*-test established that a parameter estimate was significantly non-zero if the value did not belong to the range between −1.96 and +1.96 with the statistical significance of 95%, assuming that the value was distributed according to a standard normal variable [30]. In the calibration of scenario 1, according to this formal test, the *βage* of model II and the *βtime* of model IV were not significant. In the calibration of scenario 2, on the other hand, the *βbundle\_cost* was significant, as well as the *βconstant* of model III and the *βbundle\_cost*, *βscenario*, and *βconstant* of model IV. In the calibration of scenario 3, the parameters were all obtained as significant except for the *βtime* of model IV.

The indicator *ρ*<sup>2</sup> was zero if two functions were equivalent, and it was one if instead a model predicted a probability equal to one when observing the choice actually made and declared by each user. Therefore, if *ρ*<sup>2</sup> was 1, the model reproduced the choices of the sample [30]. The highest *ρ*<sup>2</sup> was obtained with the specifications of IV for the three scenarios. Some calibrations had very low indicator values but are reported to provide comprehensive and comparable information across different scenarios and subscenarios.
