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
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.
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
to go to the 'Profundity of regret' page.
for a bundle of MATLAB codes, which includes code to estimate
for Bioson Biogeme µRRM estimation code to estimate shopping
for Python Biogeme µRRM estimation code to estimate shopping
for Pandas Biogene µRRM estimation code to estimate shopping
for Apollo R µRRM estimation code to estimate shopping choice
Example Data File
to download the example shopping choice data file (see
Arentze et al. 2005
for more details on the data)