验证性因子分析法

  本文主要为学习笔记的整合，记录分享的同时不做过多介绍。

1. 主要步骤

1.1 导入数据源

1.2 信度检验

1.3 效度检验

1.4 验证性因子分析

2. 源代码

2.1 数据源

new_data = {'a': {0: 3.75, 1: 3.38, 2: 3.88, 3: 2.88, 4: 2.75, 5: 2.5, 6:
                 4.25, 7: 2.88, 8: 4.12, 9: 4.25, 10: 3.25, 11: 4.38, 12: 4.0, 13: 4.38, 
                  14: 3.25, 15: 4.0, 16: 4.25, 17: 4.38, 18: 3.62, 19: 3.62, 
                  20: 3.88, 21: 3.88, 22: 3.38, 23: 3.88, 24: 4.0, 25: 3.75, 
                  26: 5.75, 27: 3.5, 28: 3.38, 29: 5.62, 30: 3.62, 
                  31: 4.25, 32: 3.38, 33: 3.5, 34: 3.12,
                  35: 3.25, 36: 3.12, 37: 3.38, 38: 3.5, 39: 3.12, 40: 2.88, 
                  41: 4.0, 42: 3.75, 43: 3.12, 44: 3.88, 45: 3.62, 46: 3.0, 47: 2.62, 48: 4.25, 49: 5.88}, 
            'b': {0: 4.2, 1: 4.2, 2: 4.8, 3: 6.0, 4: 3.0, 5: 4.4, 
                  6: 4.8, 7: 4.8, 8: 7.0, 9: 7.0, 10: 5.2, 11: 6.0, 12: 6.0, 
                  13: 5.8, 14: 6.0, 15: 6.0, 16: 5.6, 17: 6.2, 18: 5.2, 19: 6.0, 
                  20: 4.8, 21: 4.8, 22: 6.0, 23: 6.8, 24: 5.4, 25: 5.0, 26: 4.2, 
                  27: 5.0, 28: 3.4, 29: 5.8, 30: 4.2, 31: 4.8, 32: 4.0, 33: 3.4, 
                  34: 4.0, 35: 3.4, 36: 3.2, 37: 3.6, 38: 3.6, 39: 2.8, 40: 5.2, 
                  41: 5.2, 42: 4.8, 43: 5.6, 44: 4.6, 45: 4.6, 46: 5.0, 47: 5.0, 48: 5.0, 49: 5.0}, 
            'c': {0: 4.5, 1: 4.88, 2: 3.12, 3: 4.12, 4: 3.38, 5: 3.62, 6: 3.75,
                  7: 5.12, 8: 7.0, 9: 5.25, 10: 5.5, 11: 6.88, 12: 5.38, 13: 5.12,
                  14: 5.62, 15: 6.88, 16: 6.0, 17: 5.75, 18: 5.75, 19: 5.75, 20: 6.0,
                  21: 6.25, 22: 5.62, 23: 6.25, 24: 4.88, 25: 4.5, 26: 4.75, 27: 5.62, 
                  28: 5.38, 29: 5.62, 30: 4.88, 31: 5.0, 32: 5.25, 33: 6.38, 34: 5.5, 
                  35: 5.62, 36: 6.88, 37: 6.38, 38: 7.0, 39: 5.62, 40: 6.75, 41: 6.75, 
                  42: 6.38, 43: 6.62, 44: 5.75, 45: 6.88, 46: 6.88, 47: 6.5, 48: 6.12, 49: 6.62}, 
            'd': {0: 4.33, 1: 4.0, 2: 3.5, 3: 3.0, 4: 3.5, 5: 3.5, 6: 4.83, 7: 4.83, 
                  8: 6.67, 9: 5.17, 10: 5.83, 11: 6.67, 12: 5.33, 13: 5.0, 14: 6.17, 
                  15: 6.5, 16: 6.5, 17: 6.5, 18: 4.83, 19: 4.5, 20: 4.83, 21: 5.33, 
                  22: 5.33, 23: 7.0, 24: 4.83, 25: 3.33, 26: 5.67, 27: 4.33, 28: 3.33, 
                  29: 4.33, 30: 5.0, 31: 3.67, 32: 5.67, 33: 6.67, 34: 5.33, 35: 6.5, 
                  36: 5.5, 37: 4.83, 38: 6.0, 39: 6.5, 40: 5.0, 41: 3.83, 42: 4.83, 43: 6.5,
                  44: 4.5, 45: 4.5, 46: 5.17, 47: 4.83, 48: 6.83, 49: 6.0},
            'e': {0: 4.8, 1: 2.2, 2: 3.2, 3: 5.0, 4: 3.0, 5: 4.8, 6: 4.4, 7: 5.2, 8: 5.4,
                  9: 5.0, 10: 5.2, 11: 5.0, 12: 5.6, 13: 5.2, 14: 5.8, 15: 6.2, 16: 5.0, 
                  17: 5.0, 18: 4.8, 19: 4.6, 20: 5.0, 21: 5.8, 22: 4.8, 23: 6.6, 24: 4.8, 
                  25: 3.6, 26: 4.4, 27: 5.4, 28: 4.8, 29: 4.2, 30: 5.4, 31: 5.2, 32: 4.8, 
                  33: 4.4, 34: 5.2, 35: 5.0, 36: 6.0, 37: 5.0, 38: 4.8, 39: 5.4, 40: 7.0, 
                  41: 6.8, 42: 4.4, 43: 6.2, 44: 5.8, 45: 5.6, 46: 6.0, 47: 6.2, 48: 5.4, 49: 6.4}, 
            'f': {0: 2.4, 1: 3.0, 2: 3.8, 3: 2.8, 4: 4.6, 5: 2.6, 6: 2.6, 7: 3.8, 8: 3.6, 
                  9: 7.0, 10: 3.2, 11: 6.6, 12: 5.0, 13: 2.8, 14: 5.6, 15: 3.6, 16: 5.6, 
                  17: 4.2, 18: 5.8, 19: 3.4, 20: 2.4, 21: 3.0, 22: 3.6, 23: 5.8, 24: 5.0, 
                  25: 3.0, 26: 5.4, 27: 4.4, 28: 4.4, 29: 3.2, 30: 5.6, 31: 5.4, 32: 3.6, 
                  33: 3.2, 34: 3.2, 35: 3.0, 36: 2.6, 37: 2.6, 38: 2.4, 39: 3.0, 40: 3.8, 
                  41: 4.6, 42: 4.0, 43: 5.2, 44: 4.8, 45: 4.6, 46: 4.2, 47: 5.2, 48: 5.4, 49: 6.4},
            'g': {0: 2.33, 1: 5.5, 2: 3.83, 3: 4.5, 4: 4.83, 5: 3.83, 6: 3.83, 
                  7: 4.17, 8: 7.0, 9: 5.83, 10: 5.67, 11: 5.83, 12: 5.67, 13: 5.33,
                  14: 6.0, 15: 4.5, 16: 6.33, 17: 5.67, 18: 5.5, 19: 6.0, 20: 5.5, 
                  21: 6.5, 22: 5.33, 23: 6.5, 24: 4.67, 25: 4.83, 26: 5.17, 27: 5.33, 
                  28: 5.0, 29: 4.83, 30: 4.83, 31: 4.33, 32: 5.5, 33: 5.67, 34: 6.17, 
                  35: 5.83, 36: 6.33, 37: 6.17, 38: 5.5, 39: 6.17, 40: 6.0, 41: 4.67, 
                  42: 4.67, 43: 5.5, 44: 4.83, 45: 4.17, 46: 3.83, 47: 5.17, 48: 5.33, 49: 5.33}}

2.2 代码

import pingouin as pg
import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
from factor_analyzer import FactorAnalyzer
from factor_analyzer.factor_analyzer import calculate_kmo
from factor_analyzer.factor_analyzer import calculate_bartlett_sphericity
 
'''
1.信度检验 2.效度检验 3.验证性因子分析
'''
# 构建变量矩阵
data  = pd.DataFrame(new_data)
test_data = np.array(new_data)
 
'''
1.信度检验：检验量表的可靠性
使用克隆巴赫系数检验，a系数类似于可决系数，一般0.7以上方能通过
传入的参数需要是datafream
'''
reliability ,t_value = pg.cronbach_alpha(data)
 
'''
2.效度检验：检验量表的有效性，即准确反应客观事物属性和特征的程度
1. 巴特利特球形检验：检验变量之间的相关程度，主要是检验相关系数矩阵是否为单位矩阵
若检验结果的P值小于0.05，说明相关系数矩阵非单位矩阵，原始变量之间存在相关性
2. KMO检验：比较变量间简单相关系数和偏相关系数的指标
KMO值介于0-1之间，其值的判定方式类似于可决系数
'''
kafa_value, p_value = calculate_bartlett_sphericity(data)
kmo_all, kmo_value = calculate_kmo(data)
 
'''
验证性因子分析:主要是描述因子矩阵中的隐性变量
'''
# 1.首先建模，传入相应的因子数量
model = FactorAnalyzer(rotation=None, n_factors=len(data.T), method='principal')
model.fit(data)
# 2.获取旋转前的数据，确定公因子的数量
# 对于var_df,一般取特征值大于1的因子，同时累计方差需要位于0.7以上
f_contribution_var = model.get_factor_variance()
var_df = pd.DataFrame()
var_df["旋转前特征值"] = f_contribution_var[0]
var_df["旋转前方差贡献率"] = f_contribution_var[1]
var_df["旋转前方差累计贡献率"] = f_contribution_var[2]
 
# 3.建立因子分析模型,使用方差最大化因子旋转方式
new_model = FactorAnalyzer(3, rotation='varimax')
zd_df = data
new_model.fit(zd_df)
# 查看每个变量的公因子方差数据和,即因子载荷系数的共同度，共同度一般大于0.3认为是效果好
com_var_df = pd.DataFrame(new_model.get_communalities(), index=zd_df.columns)
# 查看旋转后的特征值，n阶矩阵只有n个特征值
feature_df = pd.DataFrame(new_model.get_eigenvalues())
# 查看公因子与原始变量的相关系数矩阵，即因子载荷系数
corr_df = pd.DataFrame(new_model.loadings_, index=zd_df.columns)
# 查看公因子方差
index_list  =['公因子名称',"公因子特征值","公因子方差贡献率","公因子累计方差贡献率"]
factor_var = pd.DataFrame(new_model.get_factor_variance()).T
factor_var.index = ['factor_'+str(x+1) for x in range(len(factor_var))]
factor_var = factor_var.reset_index()
factor_var.columns = index_list
# 提取出来的公因子的数据
out_data = pd.DataFrame(new_model.transform(zd_df))
# 最后，明确公因子与原始因子之间的相关性
#隐藏变量可视化
df1 = pd.DataFrame(corr_df, index=zd_df.columns)
df2 = data.corr()
#绘图
plt.figure()
ax = sns.heatmap(df1, annot=True, cmap="GnBu",linewidths=0.2)
 
plt.rcParams['font.sans-serif'] = ['Microsoft YaHei']
plt.rcParams['axes.unicode_minus'] = False  # 防止中文乱码的处理
plt.title("公共因子与原始变量相关性")
plt.ylabel("原始变量")
plt.xlabel('公共因子')
 
plt.legend(loc='best')
plt.show()

2.3 结果