python 因子总方差解释 python因子数

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mob6454cc7901c3 2024-09-01 09:54:12

文章标签 python 因子总方差解释 python因子分析案例方差特征值因子分析 文章分类 Python 后端开发

因子分析用Python做的一个典型例子

一、实验目的

采用合适的数据分析方法对下面的题进行解答

python 因子总方差解释 python因子数_因子分析

二、实验要求

采用因子分析方法，根据48位应聘者的15项指标得分，选出6名最优秀的应聘者。

三、代码

importpandas as pdimportnumpy as npimportmath as mathimportnumpy as npfrom numpy import *
from scipy.stats importbartlettfrom factor_analyzer import *
importnumpy.linalg as nlgfrom sklearn.cluster importKMeansfrom matplotlib importcmimportmatplotlib.pyplot as pltdefmain():
df=pd.read_csv("./data/applicant.csv")#print(df)
df2=df.copy()print("\n原始数据:\n",df2)del df2['ID']#print(df2)
#皮尔森相关系数
df2_corr=df2.corr()print("\n相关系数:\n",df2_corr)#热力图
cmap =cm.Blues#cmap = cm.hot_r
fig=plt.figure()
ax=fig.add_subplot(111)
map= ax.imshow(df2_corr, interpolation='nearest', cmap=cmap, vmin=0, vmax=1)
plt.title('correlation coefficient--headmap')
ax.set_yticks(range(len(df2_corr.columns)))
ax.set_yticklabels(df2_corr.columns)
ax.set_xticks(range(len(df2_corr)))
ax.set_xticklabels(df2_corr.columns)
plt.colorbar(map)
plt.show()#KMO测度
defkmo(dataset_corr):
corr_inv=np.linalg.inv(dataset_corr)
nrow_inv_corr, ncol_inv_corr=dataset_corr.shape
A=np.ones((nrow_inv_corr, ncol_inv_corr))for i in range(0, nrow_inv_corr, 1):for j in range(i, ncol_inv_corr, 1):
A[i, j]= -(corr_inv[i, j]) / (math.sqrt(corr_inv[i, i] *corr_inv[j, j]))
A[j, i]=A[i, j]
dataset_corr=np.asarray(dataset_corr)
kmo_num= np.sum(np.square(dataset_corr)) -np.sum(np.square(np.diagonal(A)))
kmo_denom= kmo_num + np.sum(np.square(A)) -np.sum(np.square(np.diagonal(A)))
kmo_value= kmo_num /kmo_denomreturnkmo_valueprint("\nKMO测度:", kmo(df2_corr))#巴特利特球形检验
df2_corr1 =df2_corr.valuesprint("\n巴特利特球形检验:", bartlett(df2_corr1[0], df2_corr1[1], df2_corr1[2], df2_corr1[3], df2_corr1[4],
df2_corr1[5], df2_corr1[6], df2_corr1[7], df2_corr1[8], df2_corr1[9],
df2_corr1[10], df2_corr1[11], df2_corr1[12], df2_corr1[13], df2_corr1[14]))#求特征值和特征向量
eig_value, eigvector = nlg.eig(df2_corr) #求矩阵R的全部特征值，构成向量
eig =pd.DataFrame()
eig['names'] =df2_corr.columns
eig['eig_value'] =eig_value
eig.sort_values('eig_value', ascending=False, inplace=True)print("\n特征值\n：",eig)
eig1=pd.DataFrame(eigvector)
eig1.columns=df2_corr.columns
eig1.index=df2_corr.columnsprint("\n特征向量\n",eig1)#求公因子个数m,使用前m个特征值的比重大于85%的标准，选出了公共因子是五个
for m in range(1, 15):if eig['eig_value'][:m].sum() / eig['eig_value'].sum() >= 0.85:print("\n公因子个数:", m)break
#因子载荷阵
A = np.mat(np.zeros((15, 5)))
i=0
j=0while i < 5:
j=0while j < 15:
A[j:, i]= sqrt(eig_value[i]) *eigvector[j, i]
j= j + 1i= i + 1a=pd.DataFrame(A)
a.columns= ['factor1', 'factor2', 'factor3', 'factor4', 'factor5']
a.index=df2_corr.columnsprint("\n因子载荷阵\n", a)
fa= FactorAnalyzer(n_factors=5)
fa.loadings_=a#print(fa.loadings_)
print("\n特殊因子方差:\n", fa.get_communalities()) #特殊因子方差，因子的方差贡献度 ，反映公共因子对变量的贡献
var = fa.get_factor_variance() #给出贡献率
print("\n解释的总方差（即贡献率）:\n", var)#因子旋转
rotator =Rotator()
b=pd.DataFrame(rotator.fit_transform(fa.loadings_))
b.columns= ['factor1', 'factor2', 'factor3', 'factor4', 'factor5']
b.index=df2_corr.columnsprint("\n因子旋转:\n", b)#因子得分
X1 =np.mat(df2_corr)
X1=nlg.inv(X1)
b=np.mat(b)
factor_score=np.dot(X1, b)
factor_score=pd.DataFrame(factor_score)
factor_score.columns= ['factor1', 'factor2', 'factor3', 'factor4', 'factor5']
factor_score.index=df2_corr.columnsprint("\n因子得分：\n", factor_score)
fa_t_score=np.dot(np.mat(df2), np.mat(factor_score))print("\n应试者的五个因子得分：\n",pd.DataFrame(fa_t_score))#综合得分
wei = [[0.50092], [0.137087], [0.097055], [0.079860], [0.049277]]
fa_t_score= np.dot(fa_t_score, wei) / 0.864198fa_t_score=pd.DataFrame(fa_t_score)
fa_t_score.columns= ['综合得分']
fa_t_score.insert(0,'ID', range(1, 49))print("\n综合得分：\n", fa_t_score)print("\n综合得分：\n", fa_t_score.sort_values(by='综合得分', ascending=False).head(6))
plt.figure()
ax1=plt.subplot(111)
X=fa_t_score['ID']
Y=fa_t_score['综合得分']
plt.bar(X,Y,color="#87CEFA")#plt.bar(X, Y, color="red")
plt.title('result00')
ax1.set_xticks(range(len(fa_t_score)))
ax1.set_xticklabels(fa_t_score.index)
plt.show()
fa_t_score1=pd.DataFrame()
fa_t_score1=fa_t_score.sort_values(by='综合得分',ascending=False).head()
ax2= plt.subplot(111)
X1= fa_t_score1['ID']
Y1= fa_t_score1['综合得分']
plt.bar(X1, Y1, color="#87CEFA")#plt.bar(X1, Y1, color='red')
plt.title('result01')
plt.show()if __name__ == '__main__':
main()

四、实验步骤

（1）引入数据，数据标准化

因为数据是面试中的得分，量纲相同，并且数据的分布无异常值，所以数据可以不进行标准化。

python 因子总方差解释 python因子数_python因子分析案例_02