Examples

Travel Mode Choice

We look at the Travel Choice data as examined in Chapter 18 of [Gre17].

Preprocessing

We will process a dataset with csv and pandas. We assume that a reader has access to the Travel Choice dataset.

import csv
import requests
import pandas as pd
import numpy as np

# Preallocate 840 rows and 7 columns, which is the size of the data
# We will skip the header row
df = pd.DataFrame(index=np.arange(0, 840), columns=np.arange(0, 7))
with open(CSV_FILE_PATH) as CSV_FILE:
    cr = csv.reader(CSV_FILE)
    next(cr) # skip header
    for ix, row in enumerate(cr):
        df.loc[ix] = [int(x) for x in row]

Solving for the MLE

We can initialise the model using the model_init() method.

import mdmpy
mdm0 = mdmpy.MDM(df,   # input dataframe
                 0,    # the choice is index 0
                 4,    # there are 4 possible choices
                 [2,3])
mdm0.model_init()

Assuming that the IPOPT solver is in PATH, we can choose to simply put “IPOPT” as an argument to the model_solve() method.

mdm0.model_solve("ipopt")
beta0 = [mdm0.m.beta[idx].value for idx in mdm0.m.beta]
print(beta0)

We can also get the loglikelihood of such an outcome.

ll0 = mdm0.ll(beta0)
print(ll0)

Alternatively, we can use all of the data of the choices. Since we are not changing much, we can define it as a function.

def print_beta_vals(attr_col_indices):
    mdm = mdmpy.MDM(df,   # input dataframe
                    0,    # the choice is index 0
                    4,    # there are 4 possible choices
                    attr_col_indices # now instead we use all 4 choice-specific-data columns
                    )
    mdm.model_init()
    mdm.model_solve("ipopt")
    beta = [mdm.m.beta[idx].value for idx in mdm.m.beta]
    print(beta)
    ll = mdm.ll(beta)
    print(ll)

print_beta_vals([1, 2, 3, 4])

Full Code

import csv
import pandas as pd
import numpy as np
import mdmpy

# Preallocate 840 rows and 7 columns, which is the size of the data
# We will skip the header row
df = pd.DataFrame(index=np.arange(0, 840), columns=np.arange(0, 7))
with open(CSV_FILE_PATH) as CSV_FILE:
    cr = csv.reader(CSV_FILE)
    next(cr) # skip header
    for ix, row in enumerate(cr):
        df.loc[ix] = [int(x) for x in row]

def print_beta_vals(attr_col_indices):
    mdm = mdmpy.MDM(df,   # input dataframe
                    0,    # the choice is index 0
                    4,    # there are 4 possible choices
                    attr_col_indices # now instead we use all 4 choice-specific-data columns
                    )
    mdm.model_init()
    mdm.model_solve("ipopt")
    beta = [mdm.m.beta[idx].value for idx in mdm.m.beta]
    print(beta)
    ll = mdm.ll(beta)
    print(ll)

print_beta_vals([2, 3])

print_beta_vals([1, 2, 3, 4])

[Gre17]

William H. Greene. Econometric Analysis. Pearson, 8 edition, 2017. ISBN 0134461363. URL: https://pages.stern.nyu.edu/~wgreene/Text/econometricanalysis.htm.