301: Itinerary Choice using MNL
301: Itinerary Choice using MNL¶
import pandas as pd
import larch.numba as lx
/home/runner/work/larch/larch/larch/larch/numba/model.py:23: UserWarning:
### larch.numba is experimental, and not feature-complete ###
the first time you import on a new system, this package will
compile optimized binaries for your machine, which may take
a little while, please be patient
warnings.warn( ### EXPERIMENTAL ### )
This example is an itinerary choice model built using the example itinerary choice dataset included with Larch. We’ll begin by loading that example data.
d = lx.Dataset.construct.from_idce(
pd.read_csv(lx.example_file("arc"), index_col=['id_case','id_alt']),
)
Now let’s make our model. We’ll use a few variables to define our linear-in-parameters utility function.
m = lx.Model(datatree=d)
v = [
"timeperiod==2",
"timeperiod==3",
"timeperiod==4",
"timeperiod==5",
"timeperiod==6",
"timeperiod==7",
"timeperiod==8",
"timeperiod==9",
"carrier==2",
"carrier==3",
"carrier==4",
"carrier==5",
"equipment==2",
"fare_hy",
"fare_ly",
"elapsed_time",
"nb_cnxs",
]
The larch.roles module defines a few convenient classes for declaring data and parameter.
One we will use here is PX which creates a linear-in-parameter term that represents one data
element (a column from our data, or an expression that can be evaluated on the data alone) multiplied
by a parameter with the same name.
from larch.roles import PX
m.utility_ca = sum(PX(i) for i in v)
m.choice_ca_var = 'choice'
m.availability_var = 1
Since we are estimating just an MNL model in this example, this is all we need to do to build our model, and we’re ready to go. To estimate the likelihood maximizing parameters, we give:
m.maximize_loglike()
Iteration 011 [Optimization terminated successfully.]
Best LL = -777770.0688722525
| value | initvalue | nullvalue | minimum | maximum | holdfast | note | best | |
|---|---|---|---|---|---|---|---|---|
| carrier==2 | 0.117200 | 0.0 | 0.0 | -inf | inf | 0 | 0.117200 | |
| carrier==3 | 0.638554 | 0.0 | 0.0 | -inf | inf | 0 | 0.638554 | |
| carrier==4 | 0.565252 | 0.0 | 0.0 | -inf | inf | 0 | 0.565252 | |
| carrier==5 | -0.624022 | 0.0 | 0.0 | -inf | inf | 0 | -0.624022 | |
| elapsed_time | -0.006087 | 0.0 | 0.0 | -inf | inf | 0 | -0.006087 | |
| equipment==2 | 0.466305 | 0.0 | 0.0 | -inf | inf | 0 | 0.466305 | |
| fare_hy | -0.001175 | 0.0 | 0.0 | -inf | inf | 0 | -0.001175 | |
| fare_ly | -0.001177 | 0.0 | 0.0 | -inf | inf | 0 | -0.001177 | |
| nb_cnxs | -2.947153 | 0.0 | 0.0 | -inf | inf | 0 | -2.947153 | |
| timeperiod==2 | 0.095949 | 0.0 | 0.0 | -inf | inf | 0 | 0.095949 | |
| timeperiod==3 | 0.126533 | 0.0 | 0.0 | -inf | inf | 0 | 0.126533 | |
| timeperiod==4 | 0.060552 | 0.0 | 0.0 | -inf | inf | 0 | 0.060552 | |
| timeperiod==5 | 0.140963 | 0.0 | 0.0 | -inf | inf | 0 | 0.140963 | |
| timeperiod==6 | 0.238254 | 0.0 | 0.0 | -inf | inf | 0 | 0.238254 | |
| timeperiod==7 | 0.351391 | 0.0 | 0.0 | -inf | inf | 0 | 0.351391 | |
| timeperiod==8 | 0.353302 | 0.0 | 0.0 | -inf | inf | 0 | 0.353302 | |
| timeperiod==9 | -0.010309 | 0.0 | 0.0 | -inf | inf | 0 | -0.010309 |
| key | value | ||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| loglike | -777770.0688722525 | ||||||||||||||||||||||||||||||||||||
| x |
| ||||||||||||||||||||||||||||||||||||
| tolerance | 1.3256993607330889e-06 | ||||||||||||||||||||||||||||||||||||
| steps | array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]) | ||||||||||||||||||||||||||||||||||||
| message | 'Optimization terminated successfully.' | ||||||||||||||||||||||||||||||||||||
| elapsed_time | 0:00:00.179585 | ||||||||||||||||||||||||||||||||||||
| method | 'bhhh' | ||||||||||||||||||||||||||||||||||||
| n_cases | 105 | ||||||||||||||||||||||||||||||||||||
| iteration_number | 11 | ||||||||||||||||||||||||||||||||||||
| logloss | 7407.333989259548 |