数据挖掘实例——信用评级

本次的源数据是汽车违约贷款数据集accepts.csv
原始数据与源代码可以在GitHub中下载
GitHub地址
如果有兴趣可以git clone下来自己跑一跑代码

读取源数据

import os
import numpy as np
from scipy import stats
import pandas as pd
import statsmodels.api as sm
import statsmodels.formula.api as smf
import matplotlib.pyplot as plt
accepts = pd.read_csv('accepts.csv').dropna()
accepts

衍生变量

先定义一个除法函数

def divMy(x,y):
    import numpy as np
    if x==np.nan or y==np.nan:
        return np.nan
    elif y==0:
        return -1
    else:
        return x/y
divMy(1,2)

0.5

增加变量

##历史负债收入比:tot_rev_line/tot_income
accepts["dti_hist"]=accepts[["tot_rev_line","tot_income"]].apply(lambda x:divMy(x[0],x[1]),axis = 1)
##本次新增负债收入比:loan_amt/tot_income
accepts["dti_mew"]=accepts[["loan_amt","tot_income"]].apply(lambda x:divMy(x[0],x[1]),axis = 1)
##本次贷款首付比例:down_pyt/loan_amt
accepts["fta"]=accepts[["down_pyt","loan_amt"]].apply(lambda x:divMy(x[0],x[1]),axis = 1)
##新增债务比:loan_amt/tot_rev_debt
accepts["nth"]=accepts[["loan_amt","tot_rev_debt"]].apply(lambda x:divMy(x[0],x[1]),axis = 1)
##新增债务额度比:loan_amt/tot_rev_line
accepts["nta"]=accepts[["loan_amt","tot_rev_line"]].apply(lambda x:divMy(x[0],x[1]),axis = 1)

accepts.head()

随机抽样，建立训练集与测试集

train = accepts.sample(frac=0.7, random_state=1234).copy()
test = accepts[~ accepts.index.isin(train.index)].copy()
print(' 训练集样本量: %i \n 测试集样本量: %i' %(len(train), len(test)))

训练集样本量: 2874
测试集样本量: 1231

lg = smf.glm('bad_ind ~ age_oldest_tr', data=train, 
             family=sm.families.Binomial(sm.families.links.logit)).fit()
lg.summary()
train['proba'] = lg.predict(train)
test['proba'] = lg.predict(test)

test['proba'].head(10)

4 0.238307
6 0.065840
10 0.148619
11 0.267025
13 0.283468
16 0.277072
20 0.051232
22 0.236012
35 0.147021
43 0.052479
Name: proba, dtype: float64

计算准确率

test['prediction'] = (test['proba'] > 0.3).astype('int')
pd.crosstab(test.bad_ind, test.prediction, margins=True)
acc = sum(test['prediction'] == test['bad_ind']) /np.float(len(test))
print('The accurancy is %.2f' %acc)
for i in np.arange(0.02, 0.3, 0.02):
    prediction = (test['proba'] > i).astype('int')
    confusion_matrix = pd.crosstab(prediction,test.bad_ind,
                                   margins = True)
    precision = confusion_matrix.ix[0, 0] /confusion_matrix.ix['All', 0]
    recall = confusion_matrix.ix[0, 0] / confusion_matrix.ix[0, 'All']
    Specificity = confusion_matrix.ix[1, 1] /confusion_matrix.ix[1,'All']
    f1_score = 2 * (precision * recall) / (precision + recall)
    print('threshold: %s, precision: %.2f, recall:%.2f ,Specificity:%.2f , f1_score:%.2f'%(i, precision, recall, Specificity,f1_score))

The accurancy is 0.77
threshold: 0.02, precision: 0.00, recall:1.00 ,Specificity:0.19 , f1_score:0.01
threshold: 0.04, precision: 0.02, recall:0.94 ,Specificity:0.19 , f1_score:0.03
threshold: 0.06, precision: 0.05, recall:0.91 ,Specificity:0.19 , f1_score:0.10
threshold: 0.08, precision: 0.09, recall:0.89 ,Specificity:0.19 , f1_score:0.16
threshold: 0.1, precision: 0.14, recall:0.88 ,Specificity:0.20 , f1_score:0.25
threshold: 0.12000000000000001, precision: 0.22, recall:0.89 ,Specificity:0.20 , f1_score:0.35
threshold: 0.13999999999999999, precision: 0.29, recall:0.89 ,Specificity:0.21 , f1_score:0.43
threshold: 0.16, precision: 0.38, recall:0.88 ,Specificity:0.22 , f1_score:0.53
threshold: 0.18, precision: 0.48, recall:0.86 ,Specificity:0.23 , f1_score:0.62
threshold: 0.19999999999999998, precision: 0.58, recall:0.86 ,Specificity:0.24 , f1_score:0.69
threshold: 0.22, precision: 0.69, recall:0.85 ,Specificity:0.26 , f1_score:0.76
threshold: 0.24, precision: 0.76, recall:0.84 ,Specificity:0.26 , f1_score:0.80
threshold: 0.26, precision: 0.80, recall:0.84 ,Specificity:0.28 , f1_score:0.82
threshold: 0.28, precision: 0.85, recall:0.83 ,Specificity:0.27 , f1_score:0.84

绘制ROC曲线

import sklearn.metrics as metrics

fpr_test, tpr_test, th_test = metrics.roc_curve(test.bad_ind, test.proba)
fpr_train, tpr_train, th_train = metrics.roc_curve(train.bad_ind, train.proba)

plt.figure(figsize=[3, 3])
plt.plot(fpr_test, tpr_test, 'b--')
plt.plot(fpr_train, tpr_train, 'r-')
plt.title('ROC curve')
plt.show()

多元逻辑回归

def forward_select(data, response):
    remaining = set(data.columns)
    remaining.remove(response)
    selected = []
    current_score, best_new_score = float('inf'), float('inf')
    while remaining:
        aic_with_candidates=[]
        for candidate in remaining:
            formula = "{} ~ {}".format(
                response,' + '.join(selected + [candidate]))
            aic = smf.glm(
                formula=formula, data=data, 
                family=sm.families.Binomial(sm.families.links.logit)
            ).fit().aic
            aic_with_candidates.append((aic, candidate))
        aic_with_candidates.sort(reverse=True)
        best_new_score, best_candidate=aic_with_candidates.pop()
        if current_score > best_new_score: 
            remaining.remove(best_candidate)
            selected.append(best_candidate)
            current_score = best_new_score
            print ('aic is {},continuing!'.format(current_score))
        else:        
            print ('forward selection over!')
            break
            
    formula = "{} ~ {} ".format(response,' + '.join(selected))
    print('final formula is {}'.format(formula))
    model = smf.glm(
        formula=formula, data=data, 
        family=sm.families.Binomial(sm.families.links.logit)
    ).fit()
    return(model)

使用forward_select进行变量筛选

candidates = ['bad_ind','tot_derog','age_oldest_tr','tot_open_tr','rev_util','fico_score','loan_term','ltv',
              'veh_mileage','dti_hist','dti_mew','fta','nth','nta']
data_for_select = train[candidates]

lg_m1 = forward_select(data=data_for_select, response='bad_ind')
lg_m1.summary()

aic is 2539.65259738261,continuing!
aic is 2448.9722277457986,continuing!
aic is 2406.5983198124773,continuing!
aic is 2401.0559077596185,continuing!
aic is 2397.8249140811195,continuing!
aic is 2395.437268476122,continuing!
aic is 2394.181908138009,continuing!
aic is 2393.010378559502,continuing!
forward selection over!
final formula is bad_ind ~ fico_score + ltv + age_oldest_tr + tot_derog + nth + tot_open_tr + veh_mileage + rev_util

可以看到不显著的变量被自动删除了