The µ RRM Model
The µRRM model generalizes the RRM2010 model by allowing a parameter µ to be estimated. This parameter acts as a shape parameter, despite the fact that it is confounded with the scale. The µRRM model has three special cases: 1) the RRM2010 model, 2) the linear-additive RUM model, and 3) the P-RRM model. See Cranenburgh et al. 2015 for a more extensive description of this model.
By estimating µ we essentially estimate the shape of the attribute level regret function. The four plots in the figure below show the different shapes this function can take, depending on the size of µ. The size of µ is also informative for the degree of regret minimization behaviour imposed by the µRRM model (i.e. profundity of regret). Estimating a relatively large µ signals a relatively mild profundity of regret; while, vice versa, estimating a relatively small µ signals a relatively strong profundity of regret. Finally, it is important to note that the size of µ in the µRRM model is not in any way related to the degree of determinism of the predicted choice behaviour.
The figures show that the attribute level regret function can take different shapes. From the left to the right the size of µ increases. The outer left plot corresponds with a very small µ (i.e. µ=0,01); the outer right plot corresponds to a large µ (i.e. µ=5).

To interpret the estimated parameters it is useful to compute profundities of regret for each of the taste parameters, denoted αm. These αm show how much regret behaviour is imposed with regret to attribute m. Click here to go to the 'Profundity of regret' page.


Click her e for a bundle of MATLAB codes, which includes code to estimate µRRM-MNL models.

Bison Biogeme

Click here for Bioson Biogeme µRRM estimation code to estimate shopping choice data.

Python Biogeme

Click here for Python Biogeme µRRM estimation code to estimate shopping choice data.

Pandas Biogeme

Click here for Pandas Biogene µRRM estimation code to estimate shopping choice data.


Click here for Apollo R µRRM estimation code to estimate shopping choice data.

Example Data File

Click here to download the example shopping choice data file (see Arentze et al. 2005 for more details on the data)