# A Model for Recognizing Key Factors and Applications Thereof to Engineering

Authors: Baofeng Shi; Guotai Chi
Journal: Mathematical Problems in Engineering
 (2014)

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## Abstract

This paper presents an approach to recognize key factors in data classification. Using collinearity diagnostics to delete the factors of repeated information and Logistic regression significant discriminant to select the factors which can effectively distinguish the two kinds of samples, this paper creates a model for recognizing key factors. The proposed model is demonstrated by using the 2044 observations in finical engineering. The experimental results demonstrate that the 13 indicators such as “marital status,” “net income of borrower,” and “Engel's coefficient” are the key factors to distinguish the good customers from the bad customers. By analyzing the experimental results, the performance of the proposed model is verified. Moreover, the proposed method is simple and easy to be implemented.


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## Body

## 1. Introduction

With the advent of the era of big data, the data classifications exist in fingerprint recognition, facial recognition, customer classification, DNA identification, product category, and so forth. So it has become more and more important for researchers to find the key factors which are capable of effectively distinguishing the data. For this purpose, many mathematical models are explored as the decision support methods to classify the data.In the literature, there are two main data classification methods. Artificial intelligence method is one of the classification methods for recognizing key factors. Hu et al. proposed an adaptive multilevel kernel machine method for scene classification and experimented on two popular benchmark datasets, which demonstrated that the proposed model outperformed the original spatial PACT [1]. In order to obtain the performance of customer classification models, Finlay compared the performance of several multiple classifiers and found that Error Trimmed Boosting outperformed all other multiple classifiers on UK credit data [2]. Akkoc proposed a three stage hybrid Adaptive Neuro Fuzzy Inference System client classification model, which is based on statistical techniques and Neuro Fuzzy. The proposed model performs better than the Linear Discriminant Analysis, Logistic Regression Analysis, and Artificial Neural Network (ANN) approaches [3]. By combining the biometric fractal pattern and particle swarm optimization (PSO)-based classifier, a fingerprint recognition model was established [4]. Twala explored the predicted behavior of five classifiers for different types of noise in terms of credit risk prediction accuracy and how such accuracy could be improved by using classifier ensembles. The experimental evaluation showed that the ensemble of classifiers technique has the potential to improve prediction accuracy [5]. Chen studied the classification problem of default customers and nondefault customers by using Support Vector Machines. Experiment demonstrated that the proposed model can effectively recognize the key factors [6].Statistics and measurement method is another classification tool to solve this problem. Cǎleanu et al. studied the problems of feature extraction and classifier design in facial recognition by combining a feature extraction technique and a k-NN statistical classifier method. Experimental results showed that the approach enables them to achieve both higher classification accuracy and faster processing time [7]. Compared with conventional models such as multiple discriminant analysis, logistic regression analysis, and neural networks for the classification problems of bankrupt firms and nonbankrupt firms, Min and Lee proposed the DEA classification model [8]. Shi and Chi  studied the customer classification problem by combining correlation analysis and Probit regression. Experiment demonstrated that the proposed model can recognize the key factors which can effectively distinguish the default customers from the nondefault ones [9]. In order to distinguish good customers and bad customers, Hwang et al. established ordered semiparametric Probit customers classification model by substituting ordered semiparametric function for linear regression function [10]. Sun et al. presented a classification method for distinguishing distressed enterprises and nondistressed enterprises based on gray forecasting and pattern recognition. Then the calculating result was classified to judge state of enterprise with the pattern recognition model [11]. Because attribute interactions toward classification were not considered in the classification methods, a new nonlinear classification method with nonadditive measures was proposed. Experimental results showed that applying nonadditive measures on the classic optimization-based models could improve the classification robustness and accuracy by comparing with some popular classification methods [12]. Because the existing model-based approaches are often conceptually and numerically instable for large and complex data sets, Corander et al. considered a Bayesian model-based method for unsupervised classification of discrete valued vectors, which have certain advantages over standard solutions based on latent class models [13].Although the existing researches have made great progress, there are still some drawbacks. Firstly, the collinearity between factors cannot be excluded in the existing classification researches. Secondly, the existing models include the factors which are unable to effectively distinguish the two types of samples.The purpose of this paper is to set up a model for recognition key factors, which is based on collinearity diagnostics and Logistic regression significant discriminant. Using a Chinese state-owned commercial bank’s 2044 petty loans for farmers, the proposed model is tested by screening the key factors which can effectively distinguish the good customers from the bad ones.The rest of the paper is structured as follows. We will give the constructing principle of the model for recognition key factors in Section2. The third part is the construction steps of this model. The fourth part presents the data and the empirical results. Conclusions are given in Section 5.


## 2. The Constructing Principle of the Model for Recognizing Key Factors

(
1) The Principle of Screening Key Factors. It is obtained by the bilateral probability Pj of regression coefficient cj for every factor xji by constructing the Logistic regression model among factors xji and default state yi of customers (wherein, yi is equal to 0 denoting the ith customer is a good customer and yi is equal to 1 denoting the ith customer is a bad customer). Comparing the bilateral probability Pj with the given critical probability P0, it can distinguish whether the factor xji has an obvious effect on default state of customers. By deleting these factors that have no obvious effect on default status, it ensures that the reserved factors can effectively distinguish the bad customers from the good ones.(
2) The Principle of Eliminating Redundant Information between Factors. The more redundant factors data system includes, the more disorder the data classification results will be. This paper eliminates the repeated information of the factors by using collinearity diagnostics.Flowchart of the research methodology is shown in Figure1.Figure 1
Flowchart of the research methodology.


## 3. The Recognition Key Factors Model Based on Collinearity Diagnostics and Logistic Regression Significant Discriminant

### 3.1. Data Standardization

There are two kinds of factors in practice. One is called quantitative factors (namely, quantitative indicators) and the other is called qualitative factors (namely, qualitative indicators).(
1) The Data Standardized of Quantitative Factors. The quantitative factors include positive factors, negative factors, and interval factors. The positive factors are the factors whose values are the bigger, the better; the negative factors are the factors whose values are the smaller, the better. And the interval factors are the factors whose values are reasonable only when they lie in certain intervals.Letxji denote the standardization score of the ith observed value of the jth indicator. Let vij denote the factor data of the ith observed value of the jth indicator. Let n denote the number of observations. The standardization equations of the positive factors and the negative factors are shown as (1) and (2), respectively [12],
(1)xji=vij-min1≤i≤n(vij)max1≤i≤n(vij)-min1≤i≤n(vij),(2)xji=max1≤i≤n(vij)-vijmax1≤i≤n(vij)-min1≤i≤n(vij).Letq1 denote the left boundary of the ideal interval. Let q2 denote the right boundary of the ideal interval. The standardization of the interval factors is shown as follows [12]:
(3)xji={1-q1-vijmax(q1-min1≤i≤n(vij),max1≤i≤n(vij)-q2),vij<q1(a),1-vij-q2max(q1-min1≤i≤n(vij),max1≤i≤n(vij)-q2),vij>q2(b),1,q1≤vij≤q2(c).The meanings of the rest of letters in (3) are the same as the letters in (1).(
2) The Data Standardization of Qualitative Factors. By rational analysis and expert investigation for qualitative factors, the scoring standard of qualitative factors can be obtained.


### 3.2. Deleting the Repeated Information Factors Based on Collinearity Diagnostics

(
1) The Steps of Collinearity DiagnosticsStep 1 (building regression equation).
Letxji denote the standardization score of the ith observed value of the jth factor (i=1,…n,j=1,…,m); then the regression equation of this factor with the rest of the factors is as follows:
(4)xji=a0+a1x1i+⋯+aj-1xj-1i+aj+1xj+1i+⋯+amxmi.
The estimated valuesai can be obtained by using least squares estimation in (4). Substituting these parameters ai into (4), the estimated valuex^jiof factor xji can be obtained.Step 2 (calculating the determination coefficientRj2).
Letx-j denote the mean value of the jth indicator. Then
(5)x-j=1n∑i=1nxij.
LetRj2 denote the determination coefficient of the jth indicator. Then
(6)Rj2=∑i=1n(x^ij-x-j)2∑i=1n(xij-x-j)2.
The economic meanings of (6) are as follows. The bigger determination coefficient Rj2 is, the stronger the correlation between the jth factor and the rest of factors will be. That is to say, the rest of factors can reflect the jth factor information effectively, and the jth factor should be deleted.Step 3 (calculating the variance inflation factor VIF).
LetVIFj denote the variance inflation factor of the jth indicator. Then
(7)VIFj=11-Rj2.
The economic meanings of (7) are as follows. The variance inflation factor VIFj reflects the correlation between the jth factor and the rest of factors in the same feature layer. If the variance inflation factor VIFj is greater than 10 [14], it indicates that there is a multicollinearity between the jth factor and the rest of factors, and the jth factor should be deleted.(
2) The Standard of Collinearity Diagnostics Screening. Factors, reflecting repeated information, constitute a set, and the factors only whose variance inflation factors are smaller than 10 are reserved [14].


### 3.3. Screening the Key Factors Based on Logistic Regression Significant Discriminant

(
1) The Establishment of Logistic Regression Function. Let yi denote the data status of the ith observed value; let yi equal to 0 denote that the ith observed value belongs to the first kind of sample, for example, good sample; let yi equal to 1 denote that the ith observed value belongs to the other kind of sample, for example, bad sample. Let a and cj denote regression coefficients. Let m denote the number of factors. Let xji denote the standardization of the ith observed value of the jth indicator. Let εi denote random error. The Logistic multiple linear regression function between data status yi and factors xji is as follows [14]:
(8)logit(yi)=a+c1x1i+c2x2i+⋯+cmxmi.The function of (8): it is obtained by the bilateral probability Pj of regression coefficient cj for every factor xji by constructing the Logistic regression function between evaluation factors xji and data state yi of farmers. Comparing the bilateral probability Pj with the given critical probability P0, it can distinguish whether the factors xji have an obvious effect on data state yi. Deleting these factors that do not have an obvious effect on data status, it ensures that the reserved factors can effectively distinguish bad samples from good ones.(
2) The Standard of Logistic Regression Significant Discriminant Screening. As a matter of experience, the threshold probability P0 equals 0.05 [14].IfPj≥P0=0.05 [14], accept the assumption that the true value of regression coefficient cj corresponds to the factor xji. It indicates that probability of the true value of regression coefficient cj being zero is at least 95%. In other words, the factor xji cannot significantly distinguish the data status and it should be deleted.Conversely, ifPj<P0=0.05 [14], refuse the assumption that the true value of regression coefficient cj corresponds to the factor xji. It indicates that probability of the true value of regression coefficient cj not being zero is at least 95%. In other words, the factor xji can significantly distinguish the data status and it should be reserved.


## 3.1. Data Standardization

There are two kinds of factors in practice. One is called quantitative factors (namely, quantitative indicators) and the other is called qualitative factors (namely, qualitative indicators).(
1) The Data Standardized of Quantitative Factors. The quantitative factors include positive factors, negative factors, and interval factors. The positive factors are the factors whose values are the bigger, the better; the negative factors are the factors whose values are the smaller, the better. And the interval factors are the factors whose values are reasonable only when they lie in certain intervals.Letxji denote the standardization score of the ith observed value of the jth indicator. Let vij denote the factor data of the ith observed value of the jth indicator. Let n denote the number of observations. The standardization equations of the positive factors and the negative factors are shown as (1) and (2), respectively [12],
(1)xji=vij-min1≤i≤n(vij)max1≤i≤n(vij)-min1≤i≤n(vij),(2)xji=max1≤i≤n(vij)-vijmax1≤i≤n(vij)-min1≤i≤n(vij).Letq1 denote the left boundary of the ideal interval. Let q2 denote the right boundary of the ideal interval. The standardization of the interval factors is shown as follows [12]:
(3)xji={1-q1-vijmax(q1-min1≤i≤n(vij),max1≤i≤n(vij)-q2),vij<q1(a),1-vij-q2max(q1-min1≤i≤n(vij),max1≤i≤n(vij)-q2),vij>q2(b),1,q1≤vij≤q2(c).The meanings of the rest of letters in (3) are the same as the letters in (1).(
2) The Data Standardization of Qualitative Factors. By rational analysis and expert investigation for qualitative factors, the scoring standard of qualitative factors can be obtained.


## 3.2. Deleting the Repeated Information Factors Based on Collinearity Diagnostics

(
1) The Steps of Collinearity DiagnosticsStep 1 (building regression equation).
Letxji denote the standardization score of the ith observed value of the jth factor (i=1,…n,j=1,…,m); then the regression equation of this factor with the rest of the factors is as follows:
(4)xji=a0+a1x1i+⋯+aj-1xj-1i+aj+1xj+1i+⋯+amxmi.
The estimated valuesai can be obtained by using least squares estimation in (4). Substituting these parameters ai into (4), the estimated valuex^jiof factor xji can be obtained.Step 2 (calculating the determination coefficientRj2).
Letx-j denote the mean value of the jth indicator. Then
(5)x-j=1n∑i=1nxij.
LetRj2 denote the determination coefficient of the jth indicator. Then
(6)Rj2=∑i=1n(x^ij-x-j)2∑i=1n(xij-x-j)2.
The economic meanings of (6) are as follows. The bigger determination coefficient Rj2 is, the stronger the correlation between the jth factor and the rest of factors will be. That is to say, the rest of factors can reflect the jth factor information effectively, and the jth factor should be deleted.Step 3 (calculating the variance inflation factor VIF).
LetVIFj denote the variance inflation factor of the jth indicator. Then
(7)VIFj=11-Rj2.
The economic meanings of (7) are as follows. The variance inflation factor VIFj reflects the correlation between the jth factor and the rest of factors in the same feature layer. If the variance inflation factor VIFj is greater than 10 [14], it indicates that there is a multicollinearity between the jth factor and the rest of factors, and the jth factor should be deleted.(
2) The Standard of Collinearity Diagnostics Screening. Factors, reflecting repeated information, constitute a set, and the factors only whose variance inflation factors are smaller than 10 are reserved [14].


## 3.3. Screening the Key Factors Based on Logistic Regression Significant Discriminant

(
1) The Establishment of Logistic Regression Function. Let yi denote the data status of the ith observed value; let yi equal to 0 denote that the ith observed value belongs to the first kind of sample, for example, good sample; let yi equal to 1 denote that the ith observed value belongs to the other kind of sample, for example, bad sample. Let a and cj denote regression coefficients. Let m denote the number of factors. Let xji denote the standardization of the ith observed value of the jth indicator. Let εi denote random error. The Logistic multiple linear regression function between data status yi and factors xji is as follows [14]:
(8)logit(yi)=a+c1x1i+c2x2i+⋯+cmxmi.The function of (8): it is obtained by the bilateral probability Pj of regression coefficient cj for every factor xji by constructing the Logistic regression function between evaluation factors xji and data state yi of farmers. Comparing the bilateral probability Pj with the given critical probability P0, it can distinguish whether the factors xji have an obvious effect on data state yi. Deleting these factors that do not have an obvious effect on data status, it ensures that the reserved factors can effectively distinguish bad samples from good ones.(
2) The Standard of Logistic Regression Significant Discriminant Screening. As a matter of experience, the threshold probability P0 equals 0.05 [14].IfPj≥P0=0.05 [14], accept the assumption that the true value of regression coefficient cj corresponds to the factor xji. It indicates that probability of the true value of regression coefficient cj being zero is at least 95%. In other words, the factor xji cannot significantly distinguish the data status and it should be deleted.Conversely, ifPj<P0=0.05 [14], refuse the assumption that the true value of regression coefficient cj corresponds to the factor xji. It indicates that probability of the true value of regression coefficient cj not being zero is at least 95%. In other words, the factor xji can significantly distinguish the data status and it should be reserved.


## 4. Empirical Study

### 4.1. Samples and Data Source

(
1) Samples. In order to verify the effectiveness of the proposed model, this paper recognizes the key factors which can effectively distinguish the good customers from the bad ones by using a Chinese state-owned commercial bank’s 2044 petty loans for farmers [15]. The sample includes 1589 nondefault customers (i.e., good customers) and 455 default customers (i.e., bad customers). The distribution of customers is shown in Figure 2.Figure 2
The distribution of customers.(
2) The Establishment of Extensive Factors Set. According to the available factors from a Chinese national commercial bank [15], this paper selects 68 factors of petty loans for farmers, which includes five feature layers, that is, “basic information,” “repayment ability,” “repayment willing,” “guarantee and joint guarantee,” and “macro environment,” as shown in Column 1, 2, 5 of Table 1.Table 1
Extensive factors set.
(1) Feature layers
(2) Factors
(3) References
(4) Screening result
(5) Factors
(6) References
(7) Screening result
Basic information
Loan purpose
[9, 16, 17]
Deleted by collinearity diagnostics
Supporting population
[16, 18]
Deleted by collinearity diagnostics
Age
[3, 9, 16–25]
Reserved
Family number/labor force
[16]
Deleted by significance
Value of house owing
[9, 16, 18, 24, 25]
Number of members
[18, 24]
Marital status
[3, 9, 16, 17]
Number of labor force
[18, 22]
Education background
[3, 9, 16, 17]
Deleted by significance
⋯
⋯
⋯
Household expenses
[9, 17, 18]
Area ratio of disposable assets
[9, 16]
Unavailability delete
Repayment ability
Expenses/incomes
[16, 19, 20, 22, 23]
Reserved
Agricultural production incomes
[16, 18, 24]
Deleted by collinearity diagnostics
Nonagricultural incomes/total incomes
[16, 18, 24]
Net agricultural incomes
[16, 18, 24]
Deleted by significance
Net income of borrower
[16, 18, 24]
Total expenses
[9, 25]
Education cost of children each year
[16, 18, 24]
Deleted by significance
⋯
⋯
⋯
Agricultural production expenses
[9, 16, 17]
Total property
[16]
Unavailability delete
Repayment willingness
Private loans
[9, 16, 17]
Deleted by significance
Loaning records of borrower
[9, 16–18, 22, 24, 25]
Deleted by significance
Residential stability
[3, 16, 17]
Reserved
⋯
⋯
⋯
Residential status
[3, 9]
Social reputation status
[16, 17]
Unavailability delete
Guarantee and joint guarantee
Strength of guarantor
[9, 16, 18]
Reserved
Age of guarantor
[9, 16, 18, 25]
Deleted by significance
Marital status of guarantor
[9, 16–18, 25]
⋯
⋯
⋯
Gender of guarantor
[9, 16, 24]
Deleted by significance
Credit status of joint guarantor
[16]
Unavailability delete
Macro environment
Engel's coefficient
[9, 16, 26]
Reserved
Regional government policy
[9, 18, 25]
Deleted by collinearity diagnostics
Increasing rate of regional GDP
[9, 16, 26]
⋯
⋯
⋯
Per capita agricultural output value
[17, 23]
Technical support efforts
[9, 18, 24]
Unavailability deleteAt the beginning of screening factors, we removed 18 unavailable factors, such as “credit status of joint guarantor” and “technical support efforts.” Other 50 factors are left. The deleted factors are marked with “unavailability delete” in Column 7 of Table1.(
3) Data Source. The data in the first to 50th Row and the first to 2044th Column of Table 2 are from the farmers petty credit loan system of a Chinese national commercial bank headquarter [15]. Since there exists no missing data, we used all data without any adjustment. The default status of each customer is shown in the corresponding Column, the 51st Row of Table 2. The number “1” denotes default customers, and the number “0” denotes nondefault customers.Table 2
The original data and standardized data of factors.
(a) No.
(b) Feature layers
(c) Factors
(d) Factor type
Original data of factorsvij
Standardized data of factorsxji
Nondefault customers
Default customers
(1) M. Song
⋯
(2044) M. Xu
(2045) M. Song
⋯
(3920) D. Liu
(3921) F. Chen
⋯
(4088) M. Xu
1
Basic information
Loan purpose
Qualitative
3
⋯
3
0.600
⋯
0.600
0.600
⋯
0.600
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
14
House value
Positive
0.130
⋯
0.000
0.39
⋯
0.33
0.31
⋯
0.29
15
Repayment ability
Expenses/incomes
Positive
18.989
⋯
8.124
1.000
⋯
0.887
0.000
⋯
0.123
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
31
Expense of family’s daily life
Negative
120
⋯
8
0.737
⋯
0.534
1.000
⋯
0.001
32
Repayment willingness
Private loans
Qualitative
1.12
⋯
0.51
0.014
⋯
0.025
0.019
⋯
0.006
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
39
Repayment to net income ratio
Negative
35.28
⋯
64.84
0.688
⋯
1.000
0.991
⋯
0.426
40
Guarantee and joint guarantee
Strength of guarantor
Positive
0.066
⋯
0.009
0.041
⋯
0.157
0.347
⋯
0.005
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
45
Age of guarantor
Interval
45
⋯
36
1.000
⋯
0.059
0.094
⋯
1.000
46
Macro environment
Engel's coefficient
Negative
0.373
⋯
0.399
0.892
⋯
0.135
0.246
⋯
0.773
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
50
Regional government policy
Qualitative
1
⋯
3
1.000
⋯
0.600
0.000
⋯
0.000
51
—
Default or notyi
—
0
⋯
1
0
⋯
0
1
⋯
1Next, the key factors which can distinguish the two types of customers effectively will be selected. The classification demo result of good customers and bad customers is shown in Figure3.Figure 3
The classification demo figure of good customers and bad customers.


### 4.2. The Establishment of Recognizing Key Factors Model

#### 4.2.1. The Standardization of Factors Data

(
1) Scoring the Quantify Factors. It should be pointed out that there are two interval factors in this credit system, that is, “Consumer price index” and “Age”. The ideal interval of “Consumer price index” is [101,105] [12]. Inflation or deflation is nonexistent within this interval. The ideal interval of “Age” is [31,45] [12]. The repayment ability and repayment willingness of these customers are strong in the interval.According to the factors type in Column d of Table2, take the original data of positive factors vij from Column 1 to 2044 of Table 2 into (1), the original data of negative factors vij into (2), and the original data of interval factors vij into (3), and then the standardized data of factors xji are obtained. The results are shown in Column 2045 to 4088 of Table 2.(
2) Scoring the Qualitative Factors. The scoring standard of qualitative factors can be obtained by rational analysis, as shown in Column 2 to 6 of Table 3.Table 3
The scoring criteria of qualitative factors.
(1) No.
(2) Feature layers
(3) Factors
(4) Options number
(5) Options
(6) Scoring
1
Basic information
Education background
1
Undergraduate and above
1.00
2
2
Junior college
0.90
3
3
High school and technical secondary school
0.60
4
4
Junior high school
0.40
5
5
Primary school
0.20
6
6
Other
0.00
⋯
⋯
⋯
⋯
⋯
⋯
70
Guarantee and joint guarantee
Group membership of coguarantee
1
Friendly relations, associating frequently, very familiar, business partners or neighbors
1.00
71
2
Ordinary relations, a little familiar
0.80
72
3
Unknown
0.50According to the factor type in Columnd of Table 2, standardized scores of qualitative factors can be obtained in Table 2 based on the scoring criteria of qualitative factors in Table 3. The results are shown in Column 2045 to 4088 of Table 2.


#### 4.2.2. Deleting the Repeated Information Factors

By substituting the standardized data of factorsxji in the 2045th and the 4088th Column of Table 2 into (4)–(6), the determination coefficient Rj2 of all factors is obtained, as shown in the fourth Column of Table 4. By taking the determination coefficient Rj2 in the fourth Column of Table 4 into (7), the variance inflation factor VIFi of all factors is obtained, as shown in the fifth Column of Table 4.Table 4
Collinearity diagnostics of factors.
(1) No.
(2) Feature layers
(3) Factors
(4) Determination coefficientRj2
(5) Variance inflation factor (VIFi)
(6) Screening result of collinearity diagnostics
1
Basic information
Loan purpose
0.942
17.241
Deleted
2
Age
0.091
1.100
Reserved
⋯
⋯
⋯
⋯
⋯
14
House value
0.928
13.889
Deleted
15
Repayment ability
Expenses/incomes
0.731
3.717
Reserved
⋯
⋯
⋯
⋯
⋯
31
Expense of family’s daily life
0.199
1.248
Reserved
32
Repayment willingness
Private loans
0.063
1.067
Reserved
⋯
⋯
⋯
⋯
⋯
39
Repayment to net income ratio
0.497
1.988
Reserved
40
Guarantee and joint guarantee
Strength of guarantor
0.456
1.838
Reserved
⋯
⋯
⋯
⋯
⋯
45
Age of guarantor
0.320
1.471
Reserved
46
Macro environment
Engel's coefficient
0.265
1.361
Reserved
⋯
⋯
⋯
⋯
⋯
50
Regional government policy
0.968
31.250
DeletedAccording to the standard of collinearity diagnostics screening shown in Section3.2. (2), if the variance inflation factor VIF of an indicator is greater than 10, the indicator or factor should be deleted. In this progress, eight factors which reflect repeated information are deleted and 42 factors are reserved. The deleted factors include “Loan purpose,” “House value,” and “Regional government policy,” as shown in the sixth Column of Table 4 marked as “Deleted.”


#### 4.2.3. Screening the Key Factors

(
1) The Establishment of Logistic Regression Model. By substituting the ultimate 42 factors reserved in Table 4 into (8), the Logistic regression model between data status (i.e., default status) yi and factors xji is obtained as follows:
(9)logit(yi)=a+c1x1i+c2x2i+⋯+c42x42i.The parameteri equals 1,2,…,2044, respectively, in (9). By taking the standardized data of factors xji in Column 2045 to 4088 of Table 2 into (9), the regression coefficients cj of 42 factors and the corresponding bilateral probability Pj are obtained, as shown in Column four and five of Table 5.Table 5
Screening the key factors based on Logistic regression significant discriminant.
(1) No.
(2) Feature layers
(3) Factors
(4) Regression coefficientscj
(5) Bilateral probabilityPj
(6) Critical probabilityP0
(7) Screening result
1
Basic information
Age
−1.827
0.007
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
11
Number of labor force
2.017
0.405
Deleted
12
Repayment ability
Expenses/incomes
0.079
0.044
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
26
Expense of family’s daily life
−0.328
0.834
Deleted
27
Repayment willingness
Private loans
6.220
0.104
Deleted
⋯
⋯
⋯
⋯
0.05
⋯
33
Repayment to net income ratio
2.962
0.762
Deleted
34
Guarantee and joint guarantee
Strength of guarantor
−1.973
0.000
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
38
Age of guarantor
0.264
0.772
Deleted
39
Macro environment
Engel's coefficient
−0.152
0.018
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
42
CPI
3.211
0.336
Deleted(
2) Recognizing the Key Factors. Based on the key factors screening standard shown in Section 3.3. (2), if Pj≥P0=0.05, the factor xji cannot significantly distinguish the default status and should be deleted. On the contrary, the factor xji should be retained. And the threshold probability P0 equals 0.05 in this paper, as shown in Column 6 of Table 5.Comparing the critical probabilityP0=0.05 with data in the first Row and the fifth Column of Table 5, the bilateral probability P1 corresponding to the regression coefficient c1 of the first factor “Age” is less than the critical probability 0.05; that is, P1=0.007<P0=0.05. It indicates that the factor “Age” can significantly distinguish the default status and should be reserved. The result is marked with “Reserved” in the first Row and the seventh Column of Table 5.Similarly, comparing the critical probability 0.05 with the other data in the fifth Column of Table5, the screening results were listed in the corresponding row in the seventh Column of Table 5. The logistic regression significant discriminant screening deleted 29 factors, such as “Private loans” and “Repayment to net income ratio.”In conclusion, this paper extracts thirteen factors which can effectively distinguish good customers from bad ones, as shown in Figure4.Figure 4
The key factors to distinguish good customers and bad customers.


## 4.1. Samples and Data Source

(
1) Samples. In order to verify the effectiveness of the proposed model, this paper recognizes the key factors which can effectively distinguish the good customers from the bad ones by using a Chinese state-owned commercial bank’s 2044 petty loans for farmers [15]. The sample includes 1589 nondefault customers (i.e., good customers) and 455 default customers (i.e., bad customers). The distribution of customers is shown in Figure 2.Figure 2
The distribution of customers.(
2) The Establishment of Extensive Factors Set. According to the available factors from a Chinese national commercial bank [15], this paper selects 68 factors of petty loans for farmers, which includes five feature layers, that is, “basic information,” “repayment ability,” “repayment willing,” “guarantee and joint guarantee,” and “macro environment,” as shown in Column 1, 2, 5 of Table 1.Table 1
Extensive factors set.
(1) Feature layers
(2) Factors
(3) References
(4) Screening result
(5) Factors
(6) References
(7) Screening result
Basic information
Loan purpose
[9, 16, 17]
Deleted by collinearity diagnostics
Supporting population
[16, 18]
Deleted by collinearity diagnostics
Age
[3, 9, 16–25]
Reserved
Family number/labor force
[16]
Deleted by significance
Value of house owing
[9, 16, 18, 24, 25]
Number of members
[18, 24]
Marital status
[3, 9, 16, 17]
Number of labor force
[18, 22]
Education background
[3, 9, 16, 17]
Deleted by significance
⋯
⋯
⋯
Household expenses
[9, 17, 18]
Area ratio of disposable assets
[9, 16]
Unavailability delete
Repayment ability
Expenses/incomes
[16, 19, 20, 22, 23]
Reserved
Agricultural production incomes
[16, 18, 24]
Deleted by collinearity diagnostics
Nonagricultural incomes/total incomes
[16, 18, 24]
Net agricultural incomes
[16, 18, 24]
Deleted by significance
Net income of borrower
[16, 18, 24]
Total expenses
[9, 25]
Education cost of children each year
[16, 18, 24]
Deleted by significance
⋯
⋯
⋯
Agricultural production expenses
[9, 16, 17]
Total property
[16]
Unavailability delete
Repayment willingness
Private loans
[9, 16, 17]
Deleted by significance
Loaning records of borrower
[9, 16–18, 22, 24, 25]
Deleted by significance
Residential stability
[3, 16, 17]
Reserved
⋯
⋯
⋯
Residential status
[3, 9]
Social reputation status
[16, 17]
Unavailability delete
Guarantee and joint guarantee
Strength of guarantor
[9, 16, 18]
Reserved
Age of guarantor
[9, 16, 18, 25]
Deleted by significance
Marital status of guarantor
[9, 16–18, 25]
⋯
⋯
⋯
Gender of guarantor
[9, 16, 24]
Deleted by significance
Credit status of joint guarantor
[16]
Unavailability delete
Macro environment
Engel's coefficient
[9, 16, 26]
Reserved
Regional government policy
[9, 18, 25]
Deleted by collinearity diagnostics
Increasing rate of regional GDP
[9, 16, 26]
⋯
⋯
⋯
Per capita agricultural output value
[17, 23]
Technical support efforts
[9, 18, 24]
Unavailability deleteAt the beginning of screening factors, we removed 18 unavailable factors, such as “credit status of joint guarantor” and “technical support efforts.” Other 50 factors are left. The deleted factors are marked with “unavailability delete” in Column 7 of Table1.(
3) Data Source. The data in the first to 50th Row and the first to 2044th Column of Table 2 are from the farmers petty credit loan system of a Chinese national commercial bank headquarter [15]. Since there exists no missing data, we used all data without any adjustment. The default status of each customer is shown in the corresponding Column, the 51st Row of Table 2. The number “1” denotes default customers, and the number “0” denotes nondefault customers.Table 2
The original data and standardized data of factors.
(a) No.
(b) Feature layers
(c) Factors
(d) Factor type
Original data of factorsvij
Standardized data of factorsxji
Nondefault customers
Default customers
(1) M. Song
⋯
(2044) M. Xu
(2045) M. Song
⋯
(3920) D. Liu
(3921) F. Chen
⋯
(4088) M. Xu
1
Basic information
Loan purpose
Qualitative
3
⋯
3
0.600
⋯
0.600
0.600
⋯
0.600
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
14
House value
Positive
0.130
⋯
0.000
0.39
⋯
0.33
0.31
⋯
0.29
15
Repayment ability
Expenses/incomes
Positive
18.989
⋯
8.124
1.000
⋯
0.887
0.000
⋯
0.123
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
31
Expense of family’s daily life
Negative
120
⋯
8
0.737
⋯
0.534
1.000
⋯
0.001
32
Repayment willingness
Private loans
Qualitative
1.12
⋯
0.51
0.014
⋯
0.025
0.019
⋯
0.006
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
39
Repayment to net income ratio
Negative
35.28
⋯
64.84
0.688
⋯
1.000
0.991
⋯
0.426
40
Guarantee and joint guarantee
Strength of guarantor
Positive
0.066
⋯
0.009
0.041
⋯
0.157
0.347
⋯
0.005
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
45
Age of guarantor
Interval
45
⋯
36
1.000
⋯
0.059
0.094
⋯
1.000
46
Macro environment
Engel's coefficient
Negative
0.373
⋯
0.399
0.892
⋯
0.135
0.246
⋯
0.773
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
⋯
50
Regional government policy
Qualitative
1
⋯
3
1.000
⋯
0.600
0.000
⋯
0.000
51
—
Default or notyi
—
0
⋯
1
0
⋯
0
1
⋯
1Next, the key factors which can distinguish the two types of customers effectively will be selected. The classification demo result of good customers and bad customers is shown in Figure3.Figure 3
The classification demo figure of good customers and bad customers.


## 4.2. The Establishment of Recognizing Key Factors Model

### 4.2.1. The Standardization of Factors Data

(
1) Scoring the Quantify Factors. It should be pointed out that there are two interval factors in this credit system, that is, “Consumer price index” and “Age”. The ideal interval of “Consumer price index” is [101,105] [12]. Inflation or deflation is nonexistent within this interval. The ideal interval of “Age” is [31,45] [12]. The repayment ability and repayment willingness of these customers are strong in the interval.According to the factors type in Column d of Table2, take the original data of positive factors vij from Column 1 to 2044 of Table 2 into (1), the original data of negative factors vij into (2), and the original data of interval factors vij into (3), and then the standardized data of factors xji are obtained. The results are shown in Column 2045 to 4088 of Table 2.(
2) Scoring the Qualitative Factors. The scoring standard of qualitative factors can be obtained by rational analysis, as shown in Column 2 to 6 of Table 3.Table 3
The scoring criteria of qualitative factors.
(1) No.
(2) Feature layers
(3) Factors
(4) Options number
(5) Options
(6) Scoring
1
Basic information
Education background
1
Undergraduate and above
1.00
2
2
Junior college
0.90
3
3
High school and technical secondary school
0.60
4
4
Junior high school
0.40
5
5
Primary school
0.20
6
6
Other
0.00
⋯
⋯
⋯
⋯
⋯
⋯
70
Guarantee and joint guarantee
Group membership of coguarantee
1
Friendly relations, associating frequently, very familiar, business partners or neighbors
1.00
71
2
Ordinary relations, a little familiar
0.80
72
3
Unknown
0.50According to the factor type in Columnd of Table 2, standardized scores of qualitative factors can be obtained in Table 2 based on the scoring criteria of qualitative factors in Table 3. The results are shown in Column 2045 to 4088 of Table 2.


### 4.2.2. Deleting the Repeated Information Factors

By substituting the standardized data of factorsxji in the 2045th and the 4088th Column of Table 2 into (4)–(6), the determination coefficient Rj2 of all factors is obtained, as shown in the fourth Column of Table 4. By taking the determination coefficient Rj2 in the fourth Column of Table 4 into (7), the variance inflation factor VIFi of all factors is obtained, as shown in the fifth Column of Table 4.Table 4
Collinearity diagnostics of factors.
(1) No.
(2) Feature layers
(3) Factors
(4) Determination coefficientRj2
(5) Variance inflation factor (VIFi)
(6) Screening result of collinearity diagnostics
1
Basic information
Loan purpose
0.942
17.241
Deleted
2
Age
0.091
1.100
Reserved
⋯
⋯
⋯
⋯
⋯
14
House value
0.928
13.889
Deleted
15
Repayment ability
Expenses/incomes
0.731
3.717
Reserved
⋯
⋯
⋯
⋯
⋯
31
Expense of family’s daily life
0.199
1.248
Reserved
32
Repayment willingness
Private loans
0.063
1.067
Reserved
⋯
⋯
⋯
⋯
⋯
39
Repayment to net income ratio
0.497
1.988
Reserved
40
Guarantee and joint guarantee
Strength of guarantor
0.456
1.838
Reserved
⋯
⋯
⋯
⋯
⋯
45
Age of guarantor
0.320
1.471
Reserved
46
Macro environment
Engel's coefficient
0.265
1.361
Reserved
⋯
⋯
⋯
⋯
⋯
50
Regional government policy
0.968
31.250
DeletedAccording to the standard of collinearity diagnostics screening shown in Section3.2. (2), if the variance inflation factor VIF of an indicator is greater than 10, the indicator or factor should be deleted. In this progress, eight factors which reflect repeated information are deleted and 42 factors are reserved. The deleted factors include “Loan purpose,” “House value,” and “Regional government policy,” as shown in the sixth Column of Table 4 marked as “Deleted.”


### 4.2.3. Screening the Key Factors

(
1) The Establishment of Logistic Regression Model. By substituting the ultimate 42 factors reserved in Table 4 into (8), the Logistic regression model between data status (i.e., default status) yi and factors xji is obtained as follows:
(9)logit(yi)=a+c1x1i+c2x2i+⋯+c42x42i.The parameteri equals 1,2,…,2044, respectively, in (9). By taking the standardized data of factors xji in Column 2045 to 4088 of Table 2 into (9), the regression coefficients cj of 42 factors and the corresponding bilateral probability Pj are obtained, as shown in Column four and five of Table 5.Table 5
Screening the key factors based on Logistic regression significant discriminant.
(1) No.
(2) Feature layers
(3) Factors
(4) Regression coefficientscj
(5) Bilateral probabilityPj
(6) Critical probabilityP0
(7) Screening result
1
Basic information
Age
−1.827
0.007
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
11
Number of labor force
2.017
0.405
Deleted
12
Repayment ability
Expenses/incomes
0.079
0.044
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
26
Expense of family’s daily life
−0.328
0.834
Deleted
27
Repayment willingness
Private loans
6.220
0.104
Deleted
⋯
⋯
⋯
⋯
0.05
⋯
33
Repayment to net income ratio
2.962
0.762
Deleted
34
Guarantee and joint guarantee
Strength of guarantor
−1.973
0.000
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
38
Age of guarantor
0.264
0.772
Deleted
39
Macro environment
Engel's coefficient
−0.152
0.018
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
42
CPI
3.211
0.336
Deleted(
2) Recognizing the Key Factors. Based on the key factors screening standard shown in Section 3.3. (2), if Pj≥P0=0.05, the factor xji cannot significantly distinguish the default status and should be deleted. On the contrary, the factor xji should be retained. And the threshold probability P0 equals 0.05 in this paper, as shown in Column 6 of Table 5.Comparing the critical probabilityP0=0.05 with data in the first Row and the fifth Column of Table 5, the bilateral probability P1 corresponding to the regression coefficient c1 of the first factor “Age” is less than the critical probability 0.05; that is, P1=0.007<P0=0.05. It indicates that the factor “Age” can significantly distinguish the default status and should be reserved. The result is marked with “Reserved” in the first Row and the seventh Column of Table 5.Similarly, comparing the critical probability 0.05 with the other data in the fifth Column of Table5, the screening results were listed in the corresponding row in the seventh Column of Table 5. The logistic regression significant discriminant screening deleted 29 factors, such as “Private loans” and “Repayment to net income ratio.”In conclusion, this paper extracts thirteen factors which can effectively distinguish good customers from bad ones, as shown in Figure4.Figure 4
The key factors to distinguish good customers and bad customers.


## 4.2.1. The Standardization of Factors Data

(
1) Scoring the Quantify Factors. It should be pointed out that there are two interval factors in this credit system, that is, “Consumer price index” and “Age”. The ideal interval of “Consumer price index” is [101,105] [12]. Inflation or deflation is nonexistent within this interval. The ideal interval of “Age” is [31,45] [12]. The repayment ability and repayment willingness of these customers are strong in the interval.According to the factors type in Column d of Table2, take the original data of positive factors vij from Column 1 to 2044 of Table 2 into (1), the original data of negative factors vij into (2), and the original data of interval factors vij into (3), and then the standardized data of factors xji are obtained. The results are shown in Column 2045 to 4088 of Table 2.(
2) Scoring the Qualitative Factors. The scoring standard of qualitative factors can be obtained by rational analysis, as shown in Column 2 to 6 of Table 3.Table 3
The scoring criteria of qualitative factors.
(1) No.
(2) Feature layers
(3) Factors
(4) Options number
(5) Options
(6) Scoring
1
Basic information
Education background
1
Undergraduate and above
1.00
2
2
Junior college
0.90
3
3
High school and technical secondary school
0.60
4
4
Junior high school
0.40
5
5
Primary school
0.20
6
6
Other
0.00
⋯
⋯
⋯
⋯
⋯
⋯
70
Guarantee and joint guarantee
Group membership of coguarantee
1
Friendly relations, associating frequently, very familiar, business partners or neighbors
1.00
71
2
Ordinary relations, a little familiar
0.80
72
3
Unknown
0.50According to the factor type in Columnd of Table 2, standardized scores of qualitative factors can be obtained in Table 2 based on the scoring criteria of qualitative factors in Table 3. The results are shown in Column 2045 to 4088 of Table 2.


## 4.2.2. Deleting the Repeated Information Factors

By substituting the standardized data of factorsxji in the 2045th and the 4088th Column of Table 2 into (4)–(6), the determination coefficient Rj2 of all factors is obtained, as shown in the fourth Column of Table 4. By taking the determination coefficient Rj2 in the fourth Column of Table 4 into (7), the variance inflation factor VIFi of all factors is obtained, as shown in the fifth Column of Table 4.Table 4
Collinearity diagnostics of factors.
(1) No.
(2) Feature layers
(3) Factors
(4) Determination coefficientRj2
(5) Variance inflation factor (VIFi)
(6) Screening result of collinearity diagnostics
1
Basic information
Loan purpose
0.942
17.241
Deleted
2
Age
0.091
1.100
Reserved
⋯
⋯
⋯
⋯
⋯
14
House value
0.928
13.889
Deleted
15
Repayment ability
Expenses/incomes
0.731
3.717
Reserved
⋯
⋯
⋯
⋯
⋯
31
Expense of family’s daily life
0.199
1.248
Reserved
32
Repayment willingness
Private loans
0.063
1.067
Reserved
⋯
⋯
⋯
⋯
⋯
39
Repayment to net income ratio
0.497
1.988
Reserved
40
Guarantee and joint guarantee
Strength of guarantor
0.456
1.838
Reserved
⋯
⋯
⋯
⋯
⋯
45
Age of guarantor
0.320
1.471
Reserved
46
Macro environment
Engel's coefficient
0.265
1.361
Reserved
⋯
⋯
⋯
⋯
⋯
50
Regional government policy
0.968
31.250
DeletedAccording to the standard of collinearity diagnostics screening shown in Section3.2. (2), if the variance inflation factor VIF of an indicator is greater than 10, the indicator or factor should be deleted. In this progress, eight factors which reflect repeated information are deleted and 42 factors are reserved. The deleted factors include “Loan purpose,” “House value,” and “Regional government policy,” as shown in the sixth Column of Table 4 marked as “Deleted.”


## 4.2.3. Screening the Key Factors

(
1) The Establishment of Logistic Regression Model. By substituting the ultimate 42 factors reserved in Table 4 into (8), the Logistic regression model between data status (i.e., default status) yi and factors xji is obtained as follows:
(9)logit(yi)=a+c1x1i+c2x2i+⋯+c42x42i.The parameteri equals 1,2,…,2044, respectively, in (9). By taking the standardized data of factors xji in Column 2045 to 4088 of Table 2 into (9), the regression coefficients cj of 42 factors and the corresponding bilateral probability Pj are obtained, as shown in Column four and five of Table 5.Table 5
Screening the key factors based on Logistic regression significant discriminant.
(1) No.
(2) Feature layers
(3) Factors
(4) Regression coefficientscj
(5) Bilateral probabilityPj
(6) Critical probabilityP0
(7) Screening result
1
Basic information
Age
−1.827
0.007
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
11
Number of labor force
2.017
0.405
Deleted
12
Repayment ability
Expenses/incomes
0.079
0.044
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
26
Expense of family’s daily life
−0.328
0.834
Deleted
27
Repayment willingness
Private loans
6.220
0.104
Deleted
⋯
⋯
⋯
⋯
0.05
⋯
33
Repayment to net income ratio
2.962
0.762
Deleted
34
Guarantee and joint guarantee
Strength of guarantor
−1.973
0.000
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
38
Age of guarantor
0.264
0.772
Deleted
39
Macro environment
Engel's coefficient
−0.152
0.018
Reserved
⋯
⋯
⋯
⋯
0.05
⋯
42
CPI
3.211
0.336
Deleted(
2) Recognizing the Key Factors. Based on the key factors screening standard shown in Section 3.3. (2), if Pj≥P0=0.05, the factor xji cannot significantly distinguish the default status and should be deleted. On the contrary, the factor xji should be retained. And the threshold probability P0 equals 0.05 in this paper, as shown in Column 6 of Table 5.Comparing the critical probabilityP0=0.05 with data in the first Row and the fifth Column of Table 5, the bilateral probability P1 corresponding to the regression coefficient c1 of the first factor “Age” is less than the critical probability 0.05; that is, P1=0.007<P0=0.05. It indicates that the factor “Age” can significantly distinguish the default status and should be reserved. The result is marked with “Reserved” in the first Row and the seventh Column of Table 5.Similarly, comparing the critical probability 0.05 with the other data in the fifth Column of Table5, the screening results were listed in the corresponding row in the seventh Column of Table 5. The logistic regression significant discriminant screening deleted 29 factors, such as “Private loans” and “Repayment to net income ratio.”In conclusion, this paper extracts thirteen factors which can effectively distinguish good customers from bad ones, as shown in Figure4.Figure 4
The key factors to distinguish good customers and bad customers.


## 5. Conclusion

With the advent of the era of big data, data classification puzzles have emerged in DNA identification, fingerprint recognition, customer classification, facial recognition, and so forth. Recently, recognizing key factor methods and classifier models have been proposed for solving this problem. So it has become more and more important for researchers to find key factors which are capable of effectively distinguishing the data. To do that, many mathematical models are explored as the decision support methods to classify the data.We propose a model for recognition key factors, which is based on the combination of collinearity diagnostics and Logistic regression significant discriminant. To demonstrate the performance of the proposed model, factors screening tasks were performed by an empirical study of the 2044 observations in finical engineering. Our empirical results show that the proposed model can accurately screen the key factors, which can effectively distinguish the good customers and bad customers. Moreover, the proposed method is simple and easy to be implemented.The main contribution of this study is as follows: deleting the factors that reflect repeated information by using collinearity diagnostics and recognizing the factors which can effectively distinguish the two kinds of samples by using Logistic regression significant discriminant; this paper established a recognition key factors model for data classification.



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*Source: 862132-2014-01-08.xml*