混合logit模型python

混合Logit模型（Mixed Logit Model）是一种广义线性模型，它能够捕捉到数据中的异质性（heterogeneity），即不同个体之间的行为差异。在Python中，可以使用statsmodels和biogeme等库来估计混合Logit模型。

以下是一个使用biogeme库的例子：

import pandas as pd
import biogeme.database as db
import biogeme.biogeme as bio
import biogeme.models as models
from biogeme.expressions import Beta, DefineVariable, RandomVariable
from biogeme.models import logit, piecewiseFormula, MixedLogit

# 读取数据
data = pd.read_csv('data.csv', sep='\t')

# 创建数据库
database = db.Database('data', data)

# 定义变量
age = DefineVariable('age', data['age'])
income = DefineVariable('income', data['income'])
car = DefineVariable('car', data['car'])
train_cost = DefineVariable('train_cost', data['train_cost'])
train_time = DefineVariable('train_time', data['train_time'])
choice = DefineVariable('choice', data['choice'])

# 定义参数
b_age = Beta('b_age', 0, None, None, 0)
b_income = Beta('b_income', 0, None, None, 0)
b_car = Beta('b_car', 0, None, None, 0)
b_train_cost = Beta('b_train_cost', 0, None, None, 0)
b_train_time = Beta('b_train_time', 0, None, None, 0)
mu = Beta('mu', 1, 1, None, 0)
sigma_age = Beta('sigma_age', 1, None, None, 0)
sigma_income = Beta('sigma_income', 1, None, None, 0)
sigma_train_cost = Beta('sigma_train_cost', 1, None, None, 0)
sigma_train_time = Beta('sigma_train_time', 1, None, None, 0)

# 定义随机效应变量
omega_age = RandomVariable('omega_age')
omega_income = RandomVariable('omega_income')
omega_train_cost = RandomVariable('omega_train_cost')
omega_train_time = RandomVariable('omega_train_time')

# 定义线性模型
V1 = b_age * age + b_income * income + b_car * car + b_train_cost * train_cost + b_train_time * train_time
V2 = 0
V3 = mu + omega_age * sigma_age * age + omega_income * sigma_income * income + omega_train_cost * sigma_train_cost * train_cost + omega_train_time * sigma_train_time * train_time

# 定义选择概率
P1 = logit(V1)
P2 = logit(V2)
P3 = MixedLogit(P3, [1, 2, 3], [omega_age, omega_income, omega_train_cost, omega_train_time])

# 定义模型
logprob = models.loglogit(P1, P2, P3, choice)

# 估计参数
biogeme = bio.BIOGEME(database, logprob)
results = biogeme.estimate()

在上面的代码中，我们首先读取数据并创建数据库。然后，我们定义了模型中的变量和参数。接下来，我们定义了线性模型，并使用logit函数将其转换为选择概率。最后，我们定义了一个混合Logit模型，并将其与其他两个模型结合起来。最后，我们使用biogeme库的estimate函数来估计参数。