Python实现增长混合模型/潜在类别混合模型教程

pip install stepmix

import pandas as pd
import numpy as np
from stepmix import StepMix

# 1. 生成模拟数据
np.random.seed(42)
n_samples = 200
time = np.linspace(0, 10, 100)
data = pd.DataFrame({'time': np.tile(time, n_samples),
                     'id': np.repeat(np.arange(n_samples), 100)})

# 定义两个类别的参数
class1_intercept = 2
class1_slope = 0.5
class2_intercept = 5
class2_slope = -0.2

# 随机分配类别
class_assignment = np.random.choice([0, 1], size=n_samples, p=[0.6, 0.4])

# 生成观测值
y = []
for i in range(n_samples):
    if class_assignment[i] == 0:
        y.extend(class1_intercept + class1_slope * time + np.random.normal(0, 1, len(time)))
    else:
        y.extend(class2_intercept + class2_slope * time + np.random.normal(0, 1, len(time)))

data['y'] = y

# 2. 模型定义
# 定义混合模型
model = StepMix(n_components=2,
                measurement='gaussian_glm',  # 观测变量为高斯分布
                structural='gaussian_glm',   # 时间变量对观测变量的影响为线性
                fixed_effects=['time'])       # 将时间变量作为固定效应

# 3. 模型拟合
X = data[['time']]  # 协变量
Y = data[['y']]     # 观测变量
model.fit(X, Y)

# 4. 结果分析
# 类别概率
print("类别概率:")
print(model.get_parameters()['mixing'])

# 模型参数
print("\n模型参数:")
print(model.get_parameters()['structural'])

# 类别分配
cluster_assignment = model.predict(X, Y)
data['cluster'] = np.repeat(cluster_assignment, 100)

# 可以进一步分析每个类别的特征，例如绘制每个类别中y随time变化的曲线
import matplotlib.pyplot as plt
for cluster in data['cluster'].unique():
    cluster_data = data[data['cluster'] == cluster]
    plt.plot(cluster_data['time'], cluster_data['y'], label=f'Cluster {cluster}')

plt.xlabel('Time')
plt.ylabel('Y')
plt.title('Growth Mixture Model Results')
plt.legend()
plt.show()