MDM Py
This package is a Python implementation of
Marginal Distribution Models
(MDMs), which can be used in Discrete Choice Modelling.
Documentation
Documentation is kindly hosted by Read The Docs.
Install
This package is uploaded to PyPI. Hence,
pip install mdmpyshould work.
How to use
Simplest Case
Gradient Descent
In the simplest case, we will use the Multinomial Logit (MNL) model,
which is used as a default. Assuming numpy, scipy and pandas are
installed, we generate choice data assuming a random utility model:
from string import ascii_uppercase as letters
import pandas as pd
import scipy.stats as stats
import numpy as np
NUM_INDIV = 57
NUM_CHOICES = 3
NUM_ATTR = 4
np.random.seed(2019)
X = np.random.random((NUM_ATTR, NUM_INDIV * NUM_CHOICES))
true_beta = np.random.random(NUM_ATTR)
V = np.dot(true_beta.T, X)
V = np.reshape(V, (NUM_INDIV,NUM_CHOICES))
eps = stats.gumbel_r.rvs(size=NUM_INDIV * NUM_CHOICES)
eps = np.reshape(eps, (NUM_INDIV, NUM_CHOICES))
U = V + eps
highest_util = np.argmax(U, 1)
df = pd.DataFrame(X.T)
df['choice'] = [1 if idx == x else 0 for idx in highest_util for x in range(NUM_CHOICES)]
df['individual'] = [indiv for indiv in range(NUM_INDIV) for _ in range(NUM_CHOICES)]
df['altvar'] = [altlvl for _ in range(NUM_INDIV) for altlvl in letters[:NUM_CHOICES]]With this package, we will assume that df is the dataframe which is
simply given to us. Instead of having the code itself find out how
many individuals, choices and coefficients or attributes there are, we
will simply feed them into the class. To perform a gradient descent
with this class, we will use the grad_desc method, using the df
from above as input,
import mdmpy
# In a typical case one would load df before this line
mdm = mdmpy.MDM(df, 4, 3, [0, 1, 2, 3])
np.random.seed(4)
init_beta = np.random.random(4)
grad_beta = mdm.grad_desc(init_beta)
print(grad_beta)
# expected output [0.30238122 0.07955214 0.86779824 0.50951981]Solver
The MDM class acts as a wrapper and adds the necessary pyomo
variables and sets to model the problem, but requires a solver.
IPOPT, an
interior point solver, is recommended. If you have such a solver, it
can be called. Assuming IPOPT is being used:
import mdmpy
ipopt_exec_path = /path/to/ipopt # Replace with proper path
mdm = mdmpy.MDM(df, 4, 3, [0, 1, 2, 3])
mdm.model_init()
mdm.model_solve("ipopt",ipopt_exec_path)
print([mdm.m.beta[idx].value for idx in mdm.m.beta])
# expected output [0.30238834989235025, 0.07953888508425154, 0.8678050334295714, 0.5095096796373667]
