期货因子分析(三)

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回顾

1. 期货因子分析(二)
2. 数据源

代码

import numpy as np
import pandas as pd
from factor_analyzer import FactorAnalyzer
import matplotlib.pyplot as plt
import seaborn as sns

from typing import TYPE_CHECKING

df = pd.read_csv("bfi.csv")
# Dropping unnecessary columns
df.drop(['Unnamed: 0', 'gender', 'education', 'age'], axis=1, inplace=True)
# Dropping missing values rows
df.dropna(inplace=True)

if TYPE_CHECKING: # A
    print(df.head())

if TYPE_CHECKING: # B
    from factor_analyzer.factor_analyzer import calculate_bartlett_sphericity

    # Bartlett's test of sphericity 是用来检测观察到的变量之间是否关联, 如果检测结果在统计学上不显著, 就不能采用因子分析.
    chi_square_value, p_value = calculate_bartlett_sphericity(df)
    print(chi_square_value, p_value)  # 18170.966350869257 0.0
    # p-value=0, 表明观察到的相关矩阵不是一个identity matrix. 

if TYPE_CHECKING: # C
    from factor_analyzer.factor_analyzer import calculate_kmo

    kmo_all, kmo_model = calculate_kmo(df)
    print(kmo_model)  # 0.848539722194922
    # Value of KMO less than 0.6 is considered inadequate.(就是kmo值要大于0.6)

if TYPE_CHECKING:  # D
    # Create factor analysis object and perform factor analysis
    fa = FactorAnalyzer(25, rotation=None)
    fa.fit(df)
    # Check Eigenvalues
    ev, v = fa.get_eigenvalues()

    plt.scatter(range(1, df.shape[1] + 1), ev)
    plt.plot(range(1, df.shape[1] + 1), ev)
    plt.title('Scree Plot')
    plt.xlabel('Factors')
    plt.ylabel('Eigenvalue')
    plt.grid()
    plt.show()
    
if TYPE_CHECKING: # E
    fa = FactorAnalyzer(6, rotation="varimax")
    fa.fit(df)
    
    df_cm = pd.DataFrame(np.abs(fa.loadings_), index=df.columns)
    plt.figure(figsize=(14, 14))
    ax = sns.heatmap(df_cm, annot=True, cmap="BuPu")
    # 设置y轴的字体的大小
    ax.yaxis.set_tick_params(labelsize=15)
    plt.title('Factor Analysis', fontsize='xx-large')
    # Set y-axis label
    plt.ylabel('Sepal Width', fontsize='xx-large')
    # plt.savefig('factorAnalysis.png', dpi=500)

    plt.show(dpi=500)
    
fa = FactorAnalyzer(5, rotation="varimax")
fa.fit(df)

if TYPE_CHECKING: # F
    df_cm = pd.DataFrame(np.abs(fa.loadings_), index=df.columns)
    plt.figure(figsize=(14, 14))
    ax = sns.heatmap(df_cm, annot=True, cmap="BuPu")
    # 设置y轴的字体的大小
    ax.yaxis.set_tick_params(labelsize=15)
    plt.title('Factor Analysis', fontsize='xx-large')
    # Set y-axis label
    plt.ylabel('Sepal Width', fontsize='xx-large')
    # plt.savefig('factorAnalysis.png', dpi=500)

    plt.show(dpi=500)

print(fa.get_factor_variance()) # G

分析(代码块D)

分析因子是否有效的方式一般为特征值>1. or 累计贡献>75%
显然从scree plot 可以看到factors_num<=6

分析代码块(E)

Factor 6 has none of the high loagings for any variable and is not
easily interpretable. Its good if we take only five factors. 所以尝试factors_num=5

分析(代码块G)

总结

简单来说，该因子组合解释了42.36%的累计贡献

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