Python——因子分析（KMO检验和Bartlett’s球形检验）「建议收藏」python详细安装教程

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——因子分析（KMO检验和Bartlett's球形检验）「建议收藏」

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

import pandas as pd import numpy as np import math as math import numpy as np from numpy import * from scipy.stats import bartlett from factor_analyzer import * import numpy.linalg as nlg from sklearn.cluster import KMeans from matplotlib import cm import matplotlib.pyplot as plt def main): df=pd.read_csv"./data/applicant.csv") # printdf) df2=df.copy) print"\n原始数据:\n",df2) del df2['ID'] # printdf2) # 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_subplot111) map = ax.imshowdf2_corr, interpolation='nearest', cmap=cmap, vmin=0, vmax=1) plt.title'correlation coefficient--headmap') ax.set_yticksrangelendf2_corr.columns))) ax.set_yticklabelsdf2_corr.columns) ax.set_xticksrangelendf2_corr))) ax.set_xticklabelsdf2_corr.columns) plt.colorbarmap) plt.show) # KMO测度 def kmodataset_corr): corr_inv = np.linalg.invdataset_corr) nrow_inv_corr, ncol_inv_corr = dataset_corr.shape A = np.onesnrow_inv_corr, ncol_inv_corr)) for i in range0, nrow_inv_corr, 1): for j in rangei, ncol_inv_corr, 1): A[i, j] = -corr_inv[i, j]) / math.sqrtcorr_inv[i, i] * corr_inv[j, j])) A[j, i] = A[i, j] dataset_corr = np.asarraydataset_corr) kmo_num = np.sumnp.squaredataset_corr)) - np.sumnp.squarenp.diagonalA))) kmo_denom = kmo_num + np.sumnp.squareA)) - np.sumnp.squarenp.diagonalA))) kmo_value = kmo_num / kmo_denom return kmo_value print"\nKMO测度:", kmodf2_corr)) # 巴特利特球形检验 df2_corr1 = df2_corr.values print"\n巴特利特球形检验:", bartlettdf2_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.eigdf2_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.DataFrameeigvector) eig1.columns = df2_corr.columns eig1.index = df2_corr.columns print"\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 range1, 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.matnp.zeros15, 5))) i = 0 j = 0 while i < 5: j = 0 while j < 15: A[j:, i] = sqrteig_value[i]) * eigvector[j, i] j = j + 1 i = i + 1 a = pd.DataFrameA) a.columns = ['factor1', 'factor2', 'factor3', 'factor4', 'factor5'] a.index = df2_corr.columns print"\n因子载荷阵\n", a) fa = FactorAnalyzern_factors=5) fa.loadings_ = a # printfa.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.DataFramerotator.fit_transformfa.loadings_)) b.columns = ['factor1', 'factor2', 'factor3', 'factor4', 'factor5'] b.index = df2_corr.columns print"\n因子旋转:\n", b) # 因子得分 X1 = np.matdf2_corr) X1 = nlg.invX1) b = np.matb) factor_score = np.dotX1, b) factor_score = pd.DataFramefactor_score) factor_score.columns = ['factor1', 'factor2', 'factor3', 'factor4', 'factor5'] factor_score.index = df2_corr.columns print"\n因子得分：\n", factor_score) fa_t_score = np.dotnp.matdf2), np.matfactor_score)) print"\n应试者的五个因子得分：\n",pd.DataFramefa_t_score)) # 综合得分 wei = [[0.50092], [0.137087], [0.097055], [0.079860], [0.049277]] fa_t_score = np.dotfa_t_score, wei) / 0.864198 fa_t_score = pd.DataFramefa_t_score) fa_t_score.columns = ['综合得分'] fa_t_score.insert0, 'ID', range1, 49)) print"\n综合得分：\n", fa_t_score) print"\n综合得分：\n", fa_t_score.sort_valuesby='综合得分', ascending=False).head6)) plt.figure) ax1=plt.subplot111) X=fa_t_score['ID'] Y=fa_t_score['综合得分'] plt.barX,Y,color="#87CEFA") # plt.barX, Y, color="red") plt.title'result00') ax1.set_xticksrangelenfa_t_score))) ax1.set_xticklabelsfa_t_score.index) plt.show) fa_t_score1=pd.DataFrame) fa_t_score1=fa_t_score.sort_valuesby='综合得分',ascending=False).head) ax2 = plt.subplot111) X1 = fa_t_score1['ID'] Y1 = fa_t_score1['综合得分'] plt.barX1, Y1, color="#87CEFA") # plt.barX1, Y1, color='red') plt.title'result01') plt.show) if __name__ == '__main__': main)