Random utility models are typically based on the assumptions that individuals exhibit compensatory behaviour and that their choice sets are pre-specified. These assumptions may be unrealistic in many practical cases; in particular, it has been argued that thresholds may be part of choice-rejection mechanisms (i.e. if the threshold of any attribute for a given alternative is surpassed the alternative is rejected) and, therefore, act as explicit criteria to determine the set of feasible alternatives. We formulate a semi-compensatory two-stage discrete choice model incorporating randomly distributed thresholds for attribute acceptance. The formulation allows us to estimate the parameters of the threshold's probability distribution; these parameters can be expressed as a function of the socio-economics characteristics of the individual and the conditions under which the choice process takes place. Applying the model to real and simulated data allowed us to conclude that if thresholds exist in the population, the use of compensatory models such as Multinomial Logit or even Mixed Logit, can lead to serious errors in model estimation and, therefore, in the computation of marginal rates of substitution such as the subjective value of time, as well as in prediction. Although the Mixed Logit model can deal with random parameters allowing to treat taste differences, we found it could not be used to accommodate non-compensatory behaviour or to represent the existence of thresholds.
