A package that implements Marginal Distribution Models (MDMs)
This package is a
Python implementation of Marginal Distribution Models (MDMs), which can be used in Discrete Choice Modelling.
Documentation is kindly hosted by Read The Docs.
This package is uploaded to PyPI. Hence,
pip install mdmpy
How to use
In the simplest case, we will use the Multinomial Logit (MNL) model, which is used as a default. Assuming
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]
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]
Add documentation and more meaningful comments
- Add more type hints, especially those involving Python builtins
setup.py, and remove the dependency.
MDMclass will become a
NumPyarray rather than a dataframe.
Dataframe conversion will be turned into a utility function, likely using try-except block for imports
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