# 101: Swissmetro MNL Mode Choice¶

This example is a mode choice model built using the Swissmetro example dataset. First we can create a Model object:

m = larch.Model()


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 01 (simple logit)"


We need to identify the availability and choice variables. The Swissmetro dataset, as with all Biogeme data, is only in co format, so we must define alternative availability as an expression for each alternative, using a dictionary to map alternative codes and expressions.

m.availability_co_vars = {
1: "TRAIN_AV * (SP!=0)",
2: "SM_AV",
3: "CAR_AV * (SP!=0)",
}


In the Swissmetro example dataset, as in many discrete choice modeling applications, there is one and only one chosen alternative for each case, so the choices can be described as a single expression that evaluates to the code of the chosen alternative.

m.choice_co_code = 'CHOICE'


We will also write utility functions for each alternative. Since the data is only in co format, we must use only the utility_co form for the utility functions.

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


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_.*',),
]


Now we can prepare the data, which is available in the data warehouse that comes with Larch.

from larch.data_warehouse import example_file
import pandas


The swissmetro example models exclude some observations. We will use pandas to identify the observations we would like to keep.

keep = raw_data.eval("PURPOSE in (1,3) and CHOICE != 0")
selected_data = raw_data[keep]


When you’ve created the data you need, you can pass the dataframe to the larch.DataFrames constructor. Since the swissmetro data is in idco format, we’ll need to explicitly identify the alternative codes as well.

dfs = larch.DataFrames(selected_data, alt_codes=[1,2,3])


You might notice we have not carefully constructed this object to include only the relevant data or the various simple transformations used in the utility definition above. Larch can do this itself, if you assign this DataFrames not as the actual set of data used in model estimation, but rather as the dataservice that can be used as the source to create these computational arrays.

m.dataservice = dfs


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()
-5331.252...
>>> m.calculate_parameter_covariance()
>>> m.pf.loc['B_TIME','value']
-0.01277...
>>> m.pf.loc['B_COST','value']
-0.01083...
>>> m.pf.loc['ASC_TRAIN','value']
-0.701...
>>> m.pf.loc['ASC_CAR','value']
-0.1546...

>>> 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   -0.155  4.324e-02  -3.576       5.816e-02         -2.65...
ASC_TRAIN -0.701  5.487e-02 -12.778       8.256e-02         -8.49...
LOS      B_COST    -0.011  5.183e-04 -20.910       6.823e-04        -15.88...
B_TIME    -0.013  5.688e-04 -22.465       1.043e-03        -12.25...


Tip

m = larch.example(101)