信息熵在社会序列分析中的应用（二）：纵向熵

# 计算每个序列的纵向熵
longitudinal_entropies <- seqient(myseq)

# 标准化的纵向熵
longitudinal_entropies_norm <- seqient(myseq, norm=TRUE)

# 计算所有序列的纵向熵
long_entropies <- seqient(myseq)

# 绘制纵向熵的分布
hist(long_entropies,
     main="序列纵向熵分布",
     xlab="纵向熵值",
     col="lightblue")

# 按分组比较纵向熵
boxplot(long_entropies ~ group_variable,
        data=your_data_frame,
        main="不同群体的生命历程复杂度比较",
        xlab="群体类别",
        ylab="纵向熵")

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import entropy

# 模拟生命历程序列数据
# 假设我们有100个个体的就业状态序列
# 状态: F (全职), P (兼职), U (失业), E (继续教育)
np.random.seed(42)

# 生成示例序列数据
def generate_sequences(n_sequences=100, sequence_length=3):
    # 状态定义
    states = ['F', 'P', 'U', 'E']

    # 序列生成规则（这里是一个简化的模拟）
    sequences = []
    for _ in range(n_sequences):
        seq = []
        # 第一个时间点状态分布接近原始数据
        first_dist = [0.4, 0.1, 0.35, 0.15]
        first_state = np.random.choice(states, p=first_dist)
        seq.append(first_state)

        # 后续时间点状态转移
        for t in range(1, sequence_length):
            if seq[-1] == 'F':  # 全职工作倾向于保持
                next_state = np.random.choice(states, p=[0.8, 0.1, 0.05, 0.05])
            elif seq[-1] == 'P':  # 兼职倾向于转全职或失业
                next_state = np.random.choice(states, p=[0.5, 0.2, 0.2, 0.1])
            elif seq[-1] == 'U':  # 失业倾向于找工作或继续教育
                next_state = np.random.choice(states, p=[0.4, 0.1, 0.3, 0.2])
            else:  # 继续教育倾向于全职或继续学习
                next_state = np.random.choice(states, p=[0.4, 0.1, 0.1, 0.4])
            seq.append(next_state)

        sequences.append(seq)

    return sequences

# 计算序列的纵向熵
def calculate_longitudinal_entropy(sequences):
    # 计算每个序列的状态分布
    entropies = []
    for seq in sequences:
        # 计算序列中每个状态的分布
        unique, counts = np.unique(seq, return_counts=True)
        probabilities = counts / len(seq)

        # 计算序列的熵
        seq_entropy = entropy(probabilities, base=2)
        entropies.append(seq_entropy)

    return entropies

# 分组纵向熵计算（模拟）
def calculate_group_entropies(sequences):
    # 假设我们根据某些特征将序列分为两组
    # 这里简单地将序列随机分为两组
    np.random.seed(42)
    group_labels = np.random.choice(['Group A', 'Group B'], size=len(sequences))

    # 计算每个组的纵向熵
    group_entropies = {}
    for group in ['Group A', 'Group B']:
        group_sequences = [seq for seq, label in zip(sequences, group_labels) if label == group]
        group_entropies[group] = calculate_longitudinal_entropy(group_sequences)

    return group_entropies, group_labels

# 主分析和可视化
def main():
    # 生成序列数据
    sequences = generate_sequences()

    # 计算纵向熵
    longitudinal_entropies = calculate_longitudinal_entropy(sequences)

    # 计算分组熵
    group_entropies, group_labels = calculate_group_entropies(sequences)

    # 设置清新的配色方案
    fresh_colors = ['#7eb0d5', '#8bd3c7', '#ffb55a', '#fd7f6f', '#bd7ebe']
    plt.style.use('seaborn-v0_8-whitegrid')

    # 创建画布
    fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 10), gridspec_kw={'height_ratios': [1, 1.2]})

    # 直方图：纵向熵分布
    ax1.hist(longitudinal_entropies, bins=20, color=fresh_colors[0], edgecolor='black', alpha=0.7)
    ax1.set_title('Longitudinal Entropy Distribution of Employment Sequences', fontsize=16, pad=20)
    ax1.set_xlabel('Longitudinal Entropy', fontsize=14)
    ax1.set_ylabel('Frequency', fontsize=14)
    ax1.spines['top'].set_visible(False)
    ax1.spines['right'].set_visible(False)

    # 添加平均熵值标注
    mean_entropy = np.mean(longitudinal_entropies)
    ax1.axvline(mean_entropy, color='red', linestyle='--', linewidth=2)
    ax1.text(mean_entropy*1.1, ax1.get_ylim()[1]*0.9,
             f'Mean Entropy: {mean_entropy:.3f}',
             color='red', fontsize=12, fontweight='bold')

    # 箱线图：分组纵向熵比较
    box_data = [group_entropies['Group A'], group_entropies['Group B']]
    bp = ax2.boxplot(box_data, patch_artist=True,
                     boxprops=dict(facecolor=fresh_colors[2], alpha=0.7),
                     medianprops=dict(color='red'))
    ax2.set_title('Longitudinal Entropy Comparison between Groups', fontsize=16, pad=20)
    ax2.set_xlabel('Group', fontsize=14)
    ax2.set_ylabel('Longitudinal Entropy', fontsize=14)
    ax2.set_xticklabels(['Group A', 'Group B'])
    ax2.spines['top'].set_visible(False)
    ax2.spines['right'].set_visible(False)

    # 添加统计显著性检验（这里使用t检验作为示例）
    from scipy import stats
    t_stat, p_value = stats.ttest_ind(group_entropies['Group A'], group_entropies['Group B'])
    plt.figtext(0.5, 0.01,
                f't-test: t-statistic = {t_stat:.3f}, p-value = {p_value:.4f}',
                ha='center', fontsize=10, style='italic', color='gray')

    plt.tight_layout()
    plt.subplots_adjust(bottom=0.1)

    # 保存图形
    plt.savefig('longitudinal_entropy_analysis.png', dpi=300)
    plt.show()

    # 返回一些基本统计信息
    return {
        'mean_entropy': mean_entropy,
        'group_a_mean_entropy': np.mean(group_entropies['Group A']),
        'group_b_mean_entropy': np.mean(group_entropies['Group B']),
        't_statistic': t_stat,
        'p_value': p_value
    }

# 运行主分析
if __name__ == '__main__':
    results = main()
    print("Longitudinal Entropy Analysis Results:")
    for key, value in results.items():
        print(f"{key}: {value}")

Longitudinal Entropy Analysis Results:
mean_entropy: 0.6835589588020848
group_a_mean_entropy: 0.644976136822554
group_b_mean_entropy: 0.7138740332145732
t_statistic: -0.6216085479917747
p_value: 0.5356426595744366

# 线性回归分析影响因素
lm_result <- lm(long_entropies ~ gender + education + social_class,
                data=your_data_frame)
summary(lm_result)

# 根据纵向熵将序列分组
entropy_groups <- cut(long_entropies, breaks=3,
                     labels=c("低复杂度","中复杂度","高复杂度"))

# 绘制各组的代表序列
seqdplot(myseq, group=entropy_groups,
         main="不同复杂度组的状态分布")

# 计算序列转换率
transition_rates <- seqtrate(myseq)

# 分析转换率与纵向熵的相关性
plot(rowSums(transition_rates) ~ long_entropies,
     xlab="纵向熵", ylab="状态转换总率",
     main="复杂度与状态变化频率的关系")