Within the context of discrete choice models, defining the set of alternatives and bounds or thresholds for attributes that cannot be exceeded are issues so complex that in practice, they are commonly simplified by assuming that the available alternatives can be established arbitrarily and exogenously and that individuals make their choices compensatively through a relative valuation of attributes, without limiting the range of possible values.  These assumptions overlook that the presence of thresholds and attributes may be part of alternative choice/rejection mechanisms and, therefore, can act as explicit criteria in defining the choice set.  Several methods have been proposed to correct this problem, and a distinction can be made between those that model the set of alternatives available and those that modify the utility function so that the individuals themselves implicitly eliminate alternatives that they do not consider feasible.  This latter group includes the Constrained Multinomial Logit Model (CMNL) (Martinez et al., 2008).

This work studies the calibration of the CMNL model, which consists of a Multinomial Logit (MNL) that, through penalization functions, includes the effect of the excessive value of an attribute when it comes close to, or exceeds, a threshold, thus reducing the probability that this alternative be chosen.  This defines the availability of alternatives implicitly within the choice process.  In this paper the maximum likelihood function is analytically studied and the model is calibrated using simulated and real databases. The simulation experiments showed that in the cases where behavior is constrained, the CMNL model presents a better fit to data than the classic Multinomial Logit (MNL), and it produces more accurate predictions. We analyze some identification problems present in certain specifications of the model.