109: Swissmetro Nested Logit Mode Choice

This example is a mode choice model built using the Swissmetro example dataset. First we create the DB and Model objects. When we create the DB object, we will redefine the weight value:

d = larch.examples.SWISSMETRO()
m = larch.Model(dataservice=d)

We can attach a title to the model. The title does not affect the calculations as all; it is merely used in various output report styles.

m.title = "swissmetro example 09 (nested logit)"

We need to identify the availability and choice variables. These have been conveniently set up in the data.

m.availability_var = 'avail'
m.choice_ca_var = 'choice'

The swissmetro dataset, as with all Biogeme data, is only in co format.

from larch.roles import P,X
m.utility_co[1] = ( P.ASC_TRAIN
                  + P.B_TIME * X.TRAIN_TT
                  + P.B_COST * X("TRAIN_CO*(GA==0)") )
m.utility_co[2] = ( P.B_TIME * X.SM_TT
                  + P.B_COST * X("SM_CO*(GA==0)") )
m.utility_co[3] = ( P.ASC_CAR
                  + P.B_TIME * X.CAR_TT
                  + P.B_COST * X("CAR_CO") )

To create a new nest, we can use the new_nest command, although we’ll need to know what the alternative codes are for the alternatives in our dataset. To find out, we can do:

>>> m.dataservice.alternatives
[(1, 'Train'), (2, 'SM'), (3, 'Car')]

For this example, we want to nest together the Train and Car modes into a “existing” modes nest. It looks like those are modes 1 and 3, so we can use the new_nest command like this:

m.graph.new_node(parameter="existing", parent=m.graph.root_id, children=[1,3], name='Existing')

Larch will find all the parameters in the model, but we’d like to output them in a rational order. We can use the ordering method to do this:

m.ordering = [
        ("ASCs", 'ASC.*',),
        ("LOS", 'B_.*',),
        ("LogSums", 'existing'),
]

The swissmetro example models exclude some observations. We will use the selector to identify the observations we would like to keep. There are two selector criteria, and only cases that evaluate True for both are selected.

m.dataservice.selector = ["PURPOSE in (1,3)", "CHOICE != 0"]

We can estimate the models and check the results match up with those given by Biogeme:

>>> m.load_data()
>>> m.maximize_loglike(method='slsqp')
┣ ...Optimization terminated successfully...
>>> m.loglike()
-5236.90...
>>> m.calculate_parameter_covariance()

>>> print(m.pfo()[['value','std err','t stat','robust std err','robust t stat']])  # parameter frame, ordered
                    value    std err  t stat  robust std err  robust t stat
Category Parameter
ASCs     ASC_CAR   -0.167  3.714e-02  -4.50...   5.45...e-02       -3.06...
         ASC_TRAIN -0.512  4.518e-02 -11.33...   7.91...e-02       -6.47...
LOS      B_COST    -0.009  4.627e-04 -18.51...   6.00...e-04      -14.26...
         B_TIME    -0.009  5.699e-04 -15.76...   1.07...e-03       -8.39...
LogSums  existing   0.487  2.790e-02 -18.39...   3.89...e-02      -13.18...

Tip

If you want access to the model in this example without worrying about assembling all the code blocks together on your own, you can load a read-to-estimate copy like this:

m = larch.example(109)