The P-RRM model postulates the strongest random regret
minimization behaviour possible within the RRM modelling
framework. It is one of the two special limiting cases of the µRRM
model. See
Cranenburgh et al. 2015
for a more extensive description of this model.

The key idea behind this model is that no rejoice (i.e. the opposite of regret) is experienced when the considered alternative outperforms a competitor alternative with regard an attribute m. This, in contrast to the Classical RRM model and the µRRM model which both postulate that regrets and rejoices are experienced. The figure on the right depicts attribute level regret function of the P-RRM model.

To estimate a P-RRM model, we need to compute the so-called P-RRM X-vector, denoted x-P-RRM. Because the model is essentially linear this can be done prior to estimation. A prerequisite to do so however is that the signs of the taste parameters are known prior to estimation - which is typically the case. Once we have the P-RRM X-vector, estimation of the P-RRM model is just as simple and fast as estimation of a linear-additive RUM model.

The key idea behind this model is that no rejoice (i.e. the opposite of regret) is experienced when the considered alternative outperforms a competitor alternative with regard an attribute m. This, in contrast to the Classical RRM model and the µRRM model which both postulate that regrets and rejoices are experienced. The figure on the right depicts attribute level regret function of the P-RRM model.

To estimate a P-RRM model, we need to compute the so-called P-RRM X-vector, denoted x-P-RRM. Because the model is essentially linear this can be done prior to estimation. A prerequisite to do so however is that the signs of the taste parameters are known prior to estimation - which is typically the case. Once we have the P-RRM X-vector, estimation of the P-RRM model is just as simple and fast as estimation of a linear-additive RUM model.

The linear-additive form of the P-RRM model also makes it very
attractive from a computational perspective. As the X-vector can be
computed prior to the estimation, runtimes of the P-RRM model are
proportional with choice set size, as opposed to quadratic - which
is the case for the other RRM models.

2- Code to estimate P-RRM-MNL models