- Zeitschriftendaten
- Format
- Zeitschrift
- eISSN
- 2444-8656
- Erstveröffentlichung
- 01 Jan 2016
- Erscheinungsweise
- 2 Hefte pro Jahr
- Sprachen
- Englisch
This paper takes the credit risk management of commercial banks in China as the mainline, and puts forward a quantitative model that is suitable for the credit risk management of commercial banks in China at present – Logistic regression model, and takes a commercial bank as an example, using the regression model to conduct empirical research on the credit risk of enterprises. The estimated Logistic model was tested with confirmation samples. The results show that when the cut-off point is set to 0.5, the overall correct rate of the model for the credit risk measurement of natural persons and for enterprises reaches 84.9% and 88%, respectively. When the cut-off point is set at 0.7, the overall accuracy is 89.2%. In general, the results of credit risk measurement of bank customers by the Logistic model are quite satisfactory. The Logistic Regression model is easy to understand and efficient, so it is worth popularising and putting into practice in commercial banks in China.
MSC 2010
- 03D99
In recent years, with the reform of China’s financial system, the opening of the financial industry to the outside world, the continuous entry of foreign banks, the emergence of financial innovation and the diversification of banking business, China’s banking industry is facing a huge challenge to participate in international competition. In this situation, China’s commercial banks should learn from the international advanced credit risk management experience, research the credit risk management technology suitable for China’s banks, to narrow the gap with other countries’ banking industry and improve the overall competitiveness of China’s banking industry.
Due to the asymmetric distribution of credit risk and the difficulty in data collection, it is very difficult to measure credit risk, which is also the reason why the research of credit risk management model lags behind the market risk management model. In recent years, the research on credit risk measurement models by western banks and other institutions has improved this situation. The study of these measurement models has a great impact on the bank’s credit risk management, which makes the bank’s credit risk management from qualitative to quantitative leap. However, the current research on credit risk measurement in China is more about the application of various methods proposed by the West, to evaluate the advantages and disadvantages of various methods, thus providing a good reference for the practice of credit risk of commercial banks.
This research paper deals with the commercial banks’ credit risk management based on a comparative study of the traditional and modern credit risk measurement methods and analyses enterprise and individual credit risk using the Logistic Regression model. We try to establish a suitable credit risk measurement method for China’s banks, and put forward some suggestions for management to improve our country’s commercial bank credit assets quality, and thereby reduce credit risk, which has a practical significance.
China’s commercial banks face many forms of financial risks in the process of business operation and management, and credit risk is always the main form of bank risk. It not only has an important impact on the operation safety of commercial banks but also affects the stability of the whole financial system of a country and even the stability and coordinated development of the global economy due to the domino effect. A risk assessment system becomes the key to solving the problem. Xie et al. reviewed the credit risk indicators of supply chain finance with the method of literature induction and constructed the credit risk assessment index system of online supply chain finance of commercial banks [1]. With the development of technology, the application of the Logistic Regression model emerged as is the need of the hour.
The Logical Regression model has been developing in the research of credit risk. Lan et al. built a more scientific credit risk evaluation system through the method of step-based regression based on the actual data of rural banks in China and constructed a calculation model of default probability with the Logistic Regression model [2]. As et al. put forward the methodological hypothesis of the Logistic Regression Model and illustrated the method of using this research method to evaluate family financial decisions [3]. Chen et al. adopted the Logistic Regression method and took the borrower’s default situation as the explanatory variable to establish the borrower’s credit default risk assessment model [4]. Assef et al. used artificial neural networks (ANNS), especially multi-layer perceptrons (MLP) and radial basis functions (RBF), as well as Logistic regression (LR) statistical models to analyse the bank credit status of legal persons (non-default, default and temporary default) to assist analysts in this field in making decisions [5]. Teles et al. compared the efficiency of logistic regression and linear regression in predicting whether the credit business needs recovery [6]. Jun et al. made use of bank business data and machine learning model to realie the credit anti-fraud prediction model based on a logistic regression algorithm [7]. Using the multiple logistic regression method, Zhou et al. discussed the factors affecting online consumer financial credit and countermeasures to improve its classification efficiency, providing theoretical support for improving its risk control system [8]. Xia et al. proposed a credit rating method combining the XGBOOST algorithm with the Logistic Group-Lasso model [9]. Hirk et al. used two different connection functions to evaluate the creditworthiness of a company by assuming the multivariate normal distribution and multivariate logistic distribution of the underlying variables of ordinal number results [10].
By using the credit data provided by commercial banks and combining it with the Logistic Regression model, this paper makes an empirical study on the credit risk of enterprise loans and points out the factors that affect the credit risk of enterprise loans.
According to the information provided by the five-level classified information system of enterprise loan of a commercial bank in the province, this paper randomly selects the data of one enterprise as the forecast sample and uses it to estimate the Logistic model. To facilitate the research, this paper classifies the normal and concerned enterprises as good customers, and the happy, suspicious and loss-related enterprises as bad customers. Of the 150 forecast samples,103 are good customers and 47 are bad customers.
According to the information provided by the enterprise to the bank, I selected the quantitative indicators reflecting the solvency, operation ability, profitability and development ability of the enterprise and the qualitative indicators of the quality and management level of the enterprise’s managers as the independent variables of the model. The details of these indicators are shown in Table 1.
Properties of independent variables
| The independent variables | Nature | Definitions or thresholds | |
|---|---|---|---|
| Short-term solvency indicators | Current ratio X1 | Continuous variables | Current assets ÷ Current liabilities |
| Quick ratio X2 | Continuous variables | Quick assets ÷ Current liabilities | |
| Cash flow liability ratio X3 | Continuous variables | Net operating cash flow ÷ Current liabilities | |
| Indicators of long-term solvency | Asset-liability ratio X4 | Continuous variables | The total amount of liabilities ÷ The total assets of |
| Equity ratio X5 | Continuous variables | Liabilities ÷ Owner’s equity | |
| Shareholders’ equity ratio X6 | Continuous variables | Owner’s equity ÷ assets | |
| Interest coverage multiple X7 | Continuous variables | (Total profit + interest expense) ÷ Interest charges | |
| Operational capability index | Accounts receivable turnover X8 | Continuous variables | Net income from main business ÷ Average balance of accounts receivable |
| Deposit turnover X9 | Continuous variables | Main business cost ÷ Mean surviving balance | |
| Shareholder’s equity turnover X10 | Continuous variables | Main business revenue ÷ Average balance of shareholders’ equity | |
| Total asset turnover X11 | Continuous variables | Main business revenue ÷ Average balance of assets | |
| Profitability index | Net profit rate on sales X12 | Continuous variables | Net profit ÷ Main business revenue |
| Return on assets X13 | Continuous variables | Net profit ÷ Average balance of assets | |
| Return on shareholders’ equity X14 | Continuous variables | Net profit ÷ Average balance of shareholders’ equity | |
| Development Capability Indicators | Growth rate of net assets X15 | Continuous variables | (Owners’ equity at year end-Owners’ equity at the beginning of the year) ÷Owners’ equity at the beginning of the year |
| Growth rate of total assets X16 | Continuous variables | (Total assets at year-end-Total assets at the beginning of year) ÷ Total assets at the beginning of year | |
| Main business revenue growth rate X17 | Continuous variables | (Year-end main operating income-Main operating revenue at the beginning of the year) ÷Main operating revenue at the beginning of the year | |
| Growth rate of after-tax profits X18 | Continuous variables | (Net interest rate at year end-Net interest at the beginning of the year) ÷Net interest at the beginning of the year | |
| Qualitative indicators | Quality of key management personnel X19 | Ordered class variables | “The leaders of the enterprise have rich management experience, strong management ability, remarkable historical performance and good social reputation for personal tourism”=5 ; “Corporate leaders have strong management ability and good management experience”=4; “Business leaders have strong management ability and certain management experience”=3 ; “Business leaders have general management ability and experience”=2; “other”=1 |
| Enterprise management level X20 | Ordered class variables | “The property right is clear, the organization structure is perfect, the property system is sound”=3; “general”=2; “other”=1 |
The purpose of this paper is to establish a Logistic model to judge the credit risk of an enterprise based on the financial data provided by the enterprise and some qualitative indicators to measure the nature of the enterprise, which is represented by the probability P-value. The cut-off point selected is 0.5, that is, when the value is greater than 0.5, the default probability of the enterprise is small and the enterprise is considered as a good customer, and the code of the explained variable is y=1; when the p-value is less than 0 and.5, the default probability of the enterprise is large and the enterprise is considered as a bad customer. In this case, the code of the explained variable is y=0. The explanatory variables are the 20 indicators in the table. The Logistic Regression model thus established is as follows:
Where P is the probability that the enterprise is a good customer. Square Enter method was adopted for variable selection, and SPSS13.0 software was used for Logistic Regression analysis of the data of 150 predicted samples. The results are shown in Table 2:
Block 1: Method=Enter
| B | S.E. | Wald | df | Sig | Exp(B) | ||
|---|---|---|---|---|---|---|---|
| Step 1a | 634.012 | 444.323 | 2.036 | 1 | .154 | 2E+275 | |
| -976.358 | 654.229 | 2.227 | 1 | .136 | .000 | ||
| 9.901 | 10.752 | .848 | 1 | .357 | 19959.659 | ||
| -6.869 | 20.664 | .110 | 1 | .740 | .001 | ||
| -.700 | .468 | 2.237 | 1 | .135 | .496 | ||
| 15.918 | 17.997 | .782 | 1 | .376 | 8188569 | ||
| .012 | .023 | .258 | 1 | .612 | 1.012 | ||
| -.365 | 3.199 | .013 | 1 | .909 | .694 | ||
| -4.079 | 12.464 | .107 | 1 | .743 | .017 | ||
| -.051 | .195 | .069 | 1 | .792 | .950 | ||
| 421.878 | 335.115 | 1.585 | 1 | .208 | 2E+183 | ||
| 5.475 | 9.537 | .330 | 1 | .566 | 238.710 | ||
| 21.546 | 13.779 | 2.445 | 1 | .118 | 2E+009 | ||
| 2.252 | 4.017 | .314 | 1 | .575 | 9.509 | ||
| -.022 | .156 | .020 | 1 | .887 | .978 | ||
| 17.818 | 9.660 | 3.402 | 1 | .065 | 5E+007 | ||
| -2.940 | 3.013 | .952 | 1 | .329 | .053 | ||
| -.069 | .064 | 1.173 | 1 | .279 | .933 | ||
| 4.692 | 2.145 | 4.783 | 1 | .029 | 109.041 | ||
| 1.156 | .945 | 1.495 | 1 | .221 | 3.176 | ||
| Constant | -14.618 | 18.057 | .655 | 1 | .418 | .000 |
As the method of forcing all independent variables into the model is adopted for variable selection, it can be seen from the above table that the Wald value of each variable is small, and the corresponding probability P-value is almost all greater than the significance level of 0.05, which means that the null hypothesis should not be rejected and the linear relationship between these independent variables and Logit P is not significant. Because the model contains insignificant explanatory variables, it is necessary to filter the variables and build a new model.
Here, the Forward(LR) stepwise screening strategy is adopted, that is, variables are entered into the equation according to the score test statistics, and excluded from the equation according to the likelihood ratio chi-square under the principle of maximum likelihood estimation. The standard for adding the independent variable is set at 0.05, and the standard for deleting the independent variable is set at 0.1, that is, the probability value corresponding to the F value when the independent variable is automatically excluded from the model is 0.1. The running results are as follows (Table 3).
Block 1: Method=Forward Stepwise
| B | S.E. | Wald | df | Sig | Exp(B) | ||
|---|---|---|---|---|---|---|---|
| Step 1a | 1.331 | .238 | 31.148 | 1 | .000 | 3.783 | |
| Constant | -2.179 | .498 | 19.163 | 1 | .000 | .113 | |
| Step 2b | 8.078 | 1.784 | 20.498 | 1 | .000 | 3222.223 | |
| 1.505 | .326 | 21.337 | 1 | .000 | 4.502 | ||
| Constant | -5.303 | 1.058 | 25.140 | 1 | .000 | .005 | |
| Step 3c | 8.612 | 1.933 | 19.840 | 1 | .000 | 5496.420 | |
| 2.575 | 1.045 | 6.069 | 1 | .014 | 13.132 | ||
| 1.565 | .344 | 20.679 | 1 | .000 | 4.781 | ||
| Constant | -5.623 | 1.131 | 24.707 | 1 | .000 | .004 | |
| Step 4d | 8.742 | 2.100 | 17.327 | 1 | .000 | 6261.249 | |
| 3.053 | 1.147 | 7.092 | 1 | .008 | 21.181 | ||
| 1.414 | .346 | 16.708 | 1 | .000 | 4.113 | ||
| 1.407 | .476 | 8.726 | 1 | .003 | 4,084 | ||
| Constant | -8.125 | 1.714 | 22.461 | 1 | .000 | .000 | |
| Step 5e | 9.582 | 3.431 | 7.799 | 1 | .005 | 14507.807 | |
| 10.112 | 2.551 | 15.718 | 1 | .000 | 24542.686 | ||
| 2.996 | 1.296 | 5.343 | 1 | .021 | 20.014 | ||
| 1.442 | .367 | 15.439 | 1 | .000 | 4.228 | ||
| 1,807 | .565 | 10.215 | 1 | .001 | 6.090 | ||
| Constant | -10.309 | 2.299 | 20.112 | 1 | .000 | .000 | |
| Step 6f | 9.069 | 4.046 | 5.025 | 1 | .025 | 6684.620 | |
| 11.634 | 3.498 | 11.058 | 1 | .001 | 112847.4 | ||
| 3.484 | 1.995 | 3.051 | 1 | .081 | 32.594 | ||
| 6.081 | 2.339 | 6.760 | 1 | .009 | 437.644 | ||
| 1.600 | .439 | 13.263 | 1 | .000 | 4.952 | ||
| -1.441 | .567 | 6.466 | 1 | .011 | 4.226 | ||
| Constant | -10.717 | 2.602 | 16.962 | 1 | .000 | .000 | |
| Step 7f | 9.476 | 3.823 | 6.145 | 1 | ..013 | 13046.413 | |
| 11.407 | 3.426 | 11.087 | 1 | .001 | 89911.947 | ||
| 6.297 | 2.295 | 7.530 | 1 | .006 | 543.072 | ||
| 1.569 | .427 | 13.501 | 1 | .000 | 4.803 | ||
| 1.409 | .552 | 6.519 | 1 | .011 | 4.092 | ||
| Constant | -10.587 | 2.567 | 17.006 | 1 | .000 | .000 | |
| Step 8g | 10.142 | 4.362 | 5.405 | 1 | .020 | 25399.128 | |
| -.276 | .177 | 2.437 | 1 | .119 | .759 | ||
| 10.080 | 3.100 | 10.573 | 1 | .001 | 23855.343 | ||
| 8.276 | 2.703 | 9.377 | 1 | .002 | 3927.887 | ||
| 2.111 | .596 | 12.547 | 1 | .000 | 8.259 | ||
| -1.404 | .590 | 5.664 | 1 | .017 | 4.071 | ||
| Constant | -10.562 | 2.787 | 14.365 | 1 | .000 | .000 |
The table shows each step at which the variable has been filtered. It can be seen that the model has gone through an 8-step process of variable screening, and the independent variables that are finally included in the model are cash flow liability ratio X3, property right ratio X5, shareholder equity ratio X6, the growth rate of total assets X16, quality of main managers X19 and enterprise management level X20. In addition to the property of the six, since the twin mass ratio of Wald value card square value is less than the significance level of 0.05, 3.841, and for the rest of the five variables the Wald statistic was significant, the corresponding probability value is less than the significance level of 0.05, shows that cash flow asset-liability ratio and shareholders’ equity ratio, growth rate of total assets, the main management personnel quality and enterprise management level of all the five of them have a significant linear relationship with Logit P. As for the significant contribution of the ratio of property rights to the default of enterprises, this paper will test it in the end.
The table shows the step-by-step, grouping and chi-square values of the model and the corresponding probability values after each step of variable screening. It can be seen that the chi-square value of the model in the final step is 147.042, and the corresponding probability value is 0, which is less than the significance level of 0.05. It shows that the independent variable of the model can explain the dependent variable well, and the information provided by the independent variable can help to predict the occurrence of the event better.
Table 5 shows the indicators that reflect the goodness of fit of the model. After the screening of variables, the Nagelkerke R2 statistic value corresponding to the model finally obtained was 0.878, which was close to 1, and the Hosmer-Lemeshow unified measurement value was 2.185, which was less than the degree of freedom value of 8, and the significance level was 15.51 of the
Model Summary
| -2 Log | Cox&Snell | Nagelkerke | |
|---|---|---|---|
| Step | likelihood | R Square | R Square |
| 1 | 129.593a | .316 | 444 |
| 2 | 77.879b | .515 | 724 |
| 3 | 74.269c | .527 | 740 |
| 4 | 63.951c | .558 | 785 |
| 5 | 53.695d | .588 | 826 |
| 6 | 45.133d | .610 | 858 |
| 7 | 46.403d | .607 | 853 |
| 8 | 39.481d | .625 | 878 |
Hosmer-Lemeshow Test
| Step | Chi-square | df | sig |
|---|---|---|---|
| 1 | 7.222 | 3 | .065 |
| 2 | 9.985 | 8 | .266 |
| 3 | 5.324 | 8 | .722 |
| 4 | 1.488 | 8 | .993 |
| 5 | 1.293 | 8 | .996 |
| 6 | 2.442 | 8 | .964 |
| 7 | 2.630 | 8 | .955 |
| 8 | 2.185 | 8 | .975 |
Omnibus tests of Model Coefficients
| Chi-square | df | sig | ||
|---|---|---|---|---|
| Step 1 | Step | 140.119 | 5 | .000 |
| Block | 140.119 | 5 | .000 | |
| Model | 140.119 | 5 | .000 |
Prediction of the model when the cut-off point is 0.5
| Custom | percentage | ||
|---|---|---|---|
| Custom | Bad customer | Good customer | Correct |
| Bad customer | 18 | 6 | 75.0 |
| Good customer | 4 | 55 | 93.2 |
| Overall percentage | 88.0 | ||
The prediction of the model when the cut-off point is 0.7
| Custom | percentage | ||
|---|---|---|---|
| Custom | Bad customer | Good custome | Correct |
| Bad customer | 21 | 3 | 87.5 |
| Good custome | 6 | 53 | 89.8 |
| Overall percentage | 89.2 | ||
The property right ratio index is tested. When the property right ratio index is not included in the model, the Chi-square value of the model is as follows:
The difference in degrees of freedom is only 6-5=1. It can be seen that the difference between the model chi-square values of the two models is greater than the distribution value of 3.84 when the degree of freedom is 1 and the significance level is 0.05. Therefore, we reject the original assumption that the ratio of property rights has no significant effect on whether an enterprise defaults, that is, the ratio of property rights has a strong effect on whether an enterprise defaults.
Thus, the estimated Logistic model is as follows:
Where P is the probability that the enterprise does not default. The independent variables are cash flow liability ratio, property right ratio, shareholder equity ratio, total assets growth rate, main management personnel quality and enterprise management level.
The estimated model is tested with 83 randomly selected prediction samples, and the cut-off point is still 0.5. The test results are as follows.
As can be seen from the table, among the 24 actual bad customers, the model correctly identified 18 people and wrongly identified 6 people, with a correct rate of 75%. Among the 59 good customers, the model correctly identified 55 people and wrongly identified 4 people, with a correct rate of 93.2%. The prediction accuracy of the model is 88%. If the cut-off point is set as 0.7, that is, the predicted probability value is greater than 0.7, then the classified predicted value of the explained variable is considered to be 1, and the customer is a good customer. If the customer is less than 0.7, then the customer is considered to be a bad customer with a high probability of default. The results of testing with the estimated model are shown in the table below.
Omnibus tests of Model Coefficients
| Chi-square | df | sig | ||
|---|---|---|---|---|
| Step 1 | Step | 56.930 | 1 | .000 |
| Block | 56.930 | 1 | .000 | |
| Model | 56.930 | 1 | .000 | |
| Step 2 | Step | 51.714 | 1 | .000 |
| Block | 108.644 | 2 | .000 | |
| Model | 108.644 | 2 | .000 | |
| Step 3 | Step | 3.609 | 1 | .057 |
| Block | 112.253 | 3 | .000 | |
| Model | 112.253 | 3 | .000 | |
| Step 4 | Step | 10.319 | 1 | .001 |
| Block | 122.572 | 4 | .000 | |
| Model | 122.572 | 4 | .000 | |
| Step 5 | Step | 10.256 | 1 | .001 |
| Block | 132.828 | 5 | .000 | |
| Model | 132.828 | 5 | .000 | |
| Step 6 | Step | 8.562 | 1 | .003 |
| Block | 141.390 | 6 | .000 | |
| Model | 141.390 | 6 | .000 | |
| Step 7 | Step | -1.271 | 1 | .250 |
| Block | 140.119 | 5 | .000 | |
| Model | 140.119 | 5 | .000 | |
| Step 8 | Step | 6.922 | 1 | .009 |
| Block | 147.042 | 6 | .000 | |
| Model | 147.042 | 6 | .000 |
Fig. 1
The prediction accuracy of the model when the cut-off point is 0.5
In the table, when the cut-off point is set to 0.7, among the 24 actual bad customers, the model correctly identifies 21 and wrongly identifies 3, with a correct rate of 87.5%. Among the 59 good customers, the model correctly identified 53 people and wrongly identified 6 people, and the correct rate was 89.8%. The prediction accuracy of the model is 89.2%.
Fig. 2
The prediction accuracy of the model when the cut-off point is 0.7
In summary, when the cut-off point is 0.5, the overall prediction accuracy of the estimated model is 88%. When the cut-off point is 0.7, the overall prediction accuracy is 89.2%. The prediction result of the model is satisfactory.
In this paper, the Logistic model is used to quantitatively analyse the loan credit risks of natural persons and enterprises, to get the factors that affect the credit risks of customers. For natural person loan credit risk measurement factors are gender, educational level, health status, monthly savings, household registration, the types of loans and loan time limit, and the credit risk factors that affect corporate loans have cash dynamic asset-liability ratio, equity ratio, shareholders’ equity ratio, the growth rate of total assets of four quantitative indicators and main management personnel quality and management level of qualitative indicators. The estimated Logistic model was tested with confirmation samples. When the cut-off point is set to 0.5, the overall correct rate of credit risk measurement for natural persons and enterprises is 84.9% and 88%, respectively. When the cut-off point is set at 0.7, the overall accuracy is 89.2%. In general, the results of credit risk measurement of bank customers by the Logistic model are quite satisfactory. The Logistic Regression model is easy to understand and efficient, so it is worth popularising and putting it into practice in commercial banks in China.
Fig. 1
Fig. 2
Block 1: Method=Enter
| B | S.E. | Wald | df | Sig | Exp(B) | ||
|---|---|---|---|---|---|---|---|
| Step 1a | 634.012 | 444.323 | 2.036 | 1 | .154 | 2E+275 | |
| -976.358 | 654.229 | 2.227 | 1 | .136 | .000 | ||
| 9.901 | 10.752 | .848 | 1 | .357 | 19959.659 | ||
| -6.869 | 20.664 | .110 | 1 | .740 | .001 | ||
| -.700 | .468 | 2.237 | 1 | .135 | .496 | ||
| 15.918 | 17.997 | .782 | 1 | .376 | 8188569 | ||
| .012 | .023 | .258 | 1 | .612 | 1.012 | ||
| -.365 | 3.199 | .013 | 1 | .909 | .694 | ||
| -4.079 | 12.464 | .107 | 1 | .743 | .017 | ||
| -.051 | .195 | .069 | 1 | .792 | .950 | ||
| 421.878 | 335.115 | 1.585 | 1 | .208 | 2E+183 | ||
| 5.475 | 9.537 | .330 | 1 | .566 | 238.710 | ||
| 21.546 | 13.779 | 2.445 | 1 | .118 | 2E+009 | ||
| 2.252 | 4.017 | .314 | 1 | .575 | 9.509 | ||
| -.022 | .156 | .020 | 1 | .887 | .978 | ||
| 17.818 | 9.660 | 3.402 | 1 | .065 | 5E+007 | ||
| -2.940 | 3.013 | .952 | 1 | .329 | .053 | ||
| -.069 | .064 | 1.173 | 1 | .279 | .933 | ||
| 4.692 | 2.145 | 4.783 | 1 | .029 | 109.041 | ||
| 1.156 | .945 | 1.495 | 1 | .221 | 3.176 | ||
| Constant | -14.618 | 18.057 | .655 | 1 | .418 | .000 |
Omnibus tests of Model Coefficients
| Chi-square | df | sig | ||
|---|---|---|---|---|
| Step 1 | Step | 56.930 | 1 | .000 |
| Block | 56.930 | 1 | .000 | |
| Model | 56.930 | 1 | .000 | |
| Step 2 | Step | 51.714 | 1 | .000 |
| Block | 108.644 | 2 | .000 | |
| Model | 108.644 | 2 | .000 | |
| Step 3 | Step | 3.609 | 1 | .057 |
| Block | 112.253 | 3 | .000 | |
| Model | 112.253 | 3 | .000 | |
| Step 4 | Step | 10.319 | 1 | .001 |
| Block | 122.572 | 4 | .000 | |
| Model | 122.572 | 4 | .000 | |
| Step 5 | Step | 10.256 | 1 | .001 |
| Block | 132.828 | 5 | .000 | |
| Model | 132.828 | 5 | .000 | |
| Step 6 | Step | 8.562 | 1 | .003 |
| Block | 141.390 | 6 | .000 | |
| Model | 141.390 | 6 | .000 | |
| Step 7 | Step | -1.271 | 1 | .250 |
| Block | 140.119 | 5 | .000 | |
| Model | 140.119 | 5 | .000 | |
| Step 8 | Step | 6.922 | 1 | .009 |
| Block | 147.042 | 6 | .000 | |
| Model | 147.042 | 6 | .000 |
Properties of independent variables
| The independent variables | Nature | Definitions or thresholds | |
|---|---|---|---|
| Short-term solvency indicators | Current ratio X1 | Continuous variables | Current assets ÷ Current liabilities |
| Quick ratio X2 | Continuous variables | Quick assets ÷ Current liabilities | |
| Cash flow liability ratio X3 | Continuous variables | Net operating cash flow ÷ Current liabilities | |
| Indicators of long-term solvency | Asset-liability ratio X4 | Continuous variables | The total amount of liabilities ÷ The total assets of |
| Equity ratio X5 | Continuous variables | Liabilities ÷ Owner’s equity | |
| Shareholders’ equity ratio X6 | Continuous variables | Owner’s equity ÷ assets | |
| Interest coverage multiple X7 | Continuous variables | (Total profit + interest expense) ÷ Interest charges | |
| Operational capability index | Accounts receivable turnover X8 | Continuous variables | Net income from main business ÷ Average balance of accounts receivable |
| Deposit turnover X9 | Continuous variables | Main business cost ÷ Mean surviving balance | |
| Shareholder’s equity turnover X10 | Continuous variables | Main business revenue ÷ Average balance of shareholders’ equity | |
| Total asset turnover X11 | Continuous variables | Main business revenue ÷ Average balance of assets | |
| Profitability index | Net profit rate on sales X12 | Continuous variables | Net profit ÷ Main business revenue |
| Return on assets X13 | Continuous variables | Net profit ÷ Average balance of assets | |
| Return on shareholders’ equity X14 | Continuous variables | Net profit ÷ Average balance of shareholders’ equity | |
| Development Capability Indicators | Growth rate of net assets X15 | Continuous variables | (Owners’ equity at year end-Owners’ equity at the beginning of the year) ÷Owners’ equity at the beginning of the year |
| Growth rate of total assets X16 | Continuous variables | (Total assets at year-end-Total assets at the beginning of year) ÷ Total assets at the beginning of year | |
| Main business revenue growth rate X17 | Continuous variables | (Year-end main operating income-Main operating revenue at the beginning of the year) ÷Main operating revenue at the beginning of the year | |
| Growth rate of after-tax profits X18 | Continuous variables | (Net interest rate at year end-Net interest at the beginning of the year) ÷Net interest at the beginning of the year | |
| Qualitative indicators | Quality of key management personnel X19 | Ordered class variables | “The leaders of the enterprise have rich management experience, strong management ability, remarkable historical performance and good social reputation for personal tourism”=5 ; “Corporate leaders have strong management ability and good management experience”=4; “Business leaders have strong management ability and certain management experience”=3 ; “Business leaders have general management ability and experience”=2; “other”=1 |
| Enterprise management level X20 | Ordered class variables | “The property right is clear, the organization structure is perfect, the property system is sound”=3; “general”=2; “other”=1 |
Prediction of the model when the cut-off point is 0.5
| Custom | percentage | ||
|---|---|---|---|
| Custom | Bad customer | Good customer | Correct |
| Bad customer | 18 | 6 | 75.0 |
| Good customer | 4 | 55 | 93.2 |
| Overall percentage | 88.0 | ||
The prediction of the model when the cut-off point is 0.7
| Custom | percentage | ||
|---|---|---|---|
| Custom | Bad customer | Good custome | Correct |
| Bad customer | 21 | 3 | 87.5 |
| Good custome | 6 | 53 | 89.8 |
| Overall percentage | 89.2 | ||
Hosmer-Lemeshow Test
| Step | Chi-square | df | sig |
|---|---|---|---|
| 1 | 7.222 | 3 | .065 |
| 2 | 9.985 | 8 | .266 |
| 3 | 5.324 | 8 | .722 |
| 4 | 1.488 | 8 | .993 |
| 5 | 1.293 | 8 | .996 |
| 6 | 2.442 | 8 | .964 |
| 7 | 2.630 | 8 | .955 |
| 8 | 2.185 | 8 | .975 |
Block 1: Method=Forward Stepwise
| B | S.E. | Wald | df | Sig | Exp(B) | ||
|---|---|---|---|---|---|---|---|
| Step 1a | 1.331 | .238 | 31.148 | 1 | .000 | 3.783 | |
| Constant | -2.179 | .498 | 19.163 | 1 | .000 | .113 | |
| Step 2b | 8.078 | 1.784 | 20.498 | 1 | .000 | 3222.223 | |
| 1.505 | .326 | 21.337 | 1 | .000 | 4.502 | ||
| Constant | -5.303 | 1.058 | 25.140 | 1 | .000 | .005 | |
| Step 3c | 8.612 | 1.933 | 19.840 | 1 | .000 | 5496.420 | |
| 2.575 | 1.045 | 6.069 | 1 | .014 | 13.132 | ||
| 1.565 | .344 | 20.679 | 1 | .000 | 4.781 | ||
| Constant | -5.623 | 1.131 | 24.707 | 1 | .000 | .004 | |
| Step 4d | 8.742 | 2.100 | 17.327 | 1 | .000 | 6261.249 | |
| 3.053 | 1.147 | 7.092 | 1 | .008 | 21.181 | ||
| 1.414 | .346 | 16.708 | 1 | .000 | 4.113 | ||
| 1.407 | .476 | 8.726 | 1 | .003 | 4,084 | ||
| Constant | -8.125 | 1.714 | 22.461 | 1 | .000 | .000 | |
| Step 5e | 9.582 | 3.431 | 7.799 | 1 | .005 | 14507.807 | |
| 10.112 | 2.551 | 15.718 | 1 | .000 | 24542.686 | ||
| 2.996 | 1.296 | 5.343 | 1 | .021 | 20.014 | ||
| 1.442 | .367 | 15.439 | 1 | .000 | 4.228 | ||
| 1,807 | .565 | 10.215 | 1 | .001 | 6.090 | ||
| Constant | -10.309 | 2.299 | 20.112 | 1 | .000 | .000 | |
| Step 6f | 9.069 | 4.046 | 5.025 | 1 | .025 | 6684.620 | |
| 11.634 | 3.498 | 11.058 | 1 | .001 | 112847.4 | ||
| 3.484 | 1.995 | 3.051 | 1 | .081 | 32.594 | ||
| 6.081 | 2.339 | 6.760 | 1 | .009 | 437.644 | ||
| 1.600 | .439 | 13.263 | 1 | .000 | 4.952 | ||
| -1.441 | .567 | 6.466 | 1 | .011 | 4.226 | ||
| Constant | -10.717 | 2.602 | 16.962 | 1 | .000 | .000 | |
| Step 7f | 9.476 | 3.823 | 6.145 | 1 | ..013 | 13046.413 | |
| 11.407 | 3.426 | 11.087 | 1 | .001 | 89911.947 | ||
| 6.297 | 2.295 | 7.530 | 1 | .006 | 543.072 | ||
| 1.569 | .427 | 13.501 | 1 | .000 | 4.803 | ||
| 1.409 | .552 | 6.519 | 1 | .011 | 4.092 | ||
| Constant | -10.587 | 2.567 | 17.006 | 1 | .000 | .000 | |
| Step 8g | 10.142 | 4.362 | 5.405 | 1 | .020 | 25399.128 | |
| -.276 | .177 | 2.437 | 1 | .119 | .759 | ||
| 10.080 | 3.100 | 10.573 | 1 | .001 | 23855.343 | ||
| 8.276 | 2.703 | 9.377 | 1 | .002 | 3927.887 | ||
| 2.111 | .596 | 12.547 | 1 | .000 | 8.259 | ||
| -1.404 | .590 | 5.664 | 1 | .017 | 4.071 | ||
| Constant | -10.562 | 2.787 | 14.365 | 1 | .000 | .000 |
Model Summary
| -2 Log | Cox&Snell | Nagelkerke | |
|---|---|---|---|
| Step | likelihood | R Square | R Square |
| 1 | 129.593a | .316 | 444 |
| 2 | 77.879b | .515 | 724 |
| 3 | 74.269c | .527 | 740 |
| 4 | 63.951c | .558 | 785 |
| 5 | 53.695d | .588 | 826 |
| 6 | 45.133d | .610 | 858 |
| 7 | 46.403d | .607 | 853 |
| 8 | 39.481d | .625 | 878 |
Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Response model for the psychological education of college students based on non-linear finite element equations Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Nonlinear Differential Equations in the Teaching Model of Educational Informatisation The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe80Si10Nb6B2Cu2 Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Research on tourism income index based on ordinary differential mathematical equation Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Sports Science Teaching of Athletics Based on Nonlinear Mathematical Equation Informatisation of educational reform based on fractional differential equations Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x p m −x +δ )s +ax p m +bx overF p 2m Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Translog function in government development of low-carbon economy Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Constructing Artistic Surface Modeling Design Based on Nonlinear Over-limit Interpolation Equation Numerical Simulation Analysis Mathematics of Fluid Mechanics for Semiconductor Circuit Breaker Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Human Body Movement Coupling Model in Physical Education Class in the Educational Mathematical Equation of Reasonable Exercise Course The contribution of structural equation model analysis to higher education agglomeration and innovation and entrepreneurship Study on the evolutionary game theory of the psychological choice for online purchase of fresh produce under replicator dynamics formula The influence of X fuzzy mathematics method in basketball tactics scoring Mathematical statistics algorithm in the bending performance test of corroded reinforced concrete beams under fatigue load Nonlinear strategic human resource management based on organisational mathematical model Back propagation mathematical model for stock price prediction Evolutionary game research on the psychological choice of online shopping of fresh agricultural products based on dynamic simulation model Differential equation model of financial market stability based on big data Multi-attribute decision-making methods based on normal random variables in supply chain risk management Linear fractional differential equations in bank resource allocation and financial risk management model Construction and reform of art design teaching mode under the background of the integration of non-linear equations and the internet Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory College students’ innovation and entrepreneurship ability based on nonlinear model Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Mathematical simulation analysis of optimal testing of shot puter's throwing path Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings The term structure of economic management rate under the parameter analysis of the estimation model based on common differential equation Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data The improvement of museum information flow based on paste functional mapping method The art design of industrialised manufacturing furniture products based on the simulation of mathematical curves TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Modelling and Simulation of Collaborative Innovation System in Colleges and Universities Based on Interpreted Structural Equation Model Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts The Optimal Solution of Feature Decomposition Based on the Mathematical Model of Nonlinear Landscape Garden Features Composite mechanical performance of prefabricated concrete based on hysteresis curve equation Higher education innovation and reform model based on hierarchical probit Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot The teaching of sports science of track and field-based on nonlinear mathematical equations Visual error correction of continuous aerobics action images based on graph difference function Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Precision algorithms in second-order fractional differential equations Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Fractional differential equations in National Sports Training in Colleges and Universities Radioactive source search problem and optimisation model based on meta-heuristic algorithm Application of mathematical probabilistic statistical model of base – FFCA financial data processing Research on a method of completeness index based on complex model Distribution network monitoring and management system based on intelligent recognition and judgement Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Topological optimisation technology of gravity dam section structure based on ANSYS partial differential equation operation Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Engineering project management based on multiple regression equation and building information modelling technology Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials Mathematical model of transforming image elements to structured data based on BP neural network Educational reform informatisation based on fractional differential equation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Research on identifying psychological health problems of college students by logistic regression model based on data mining Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation A mathematical model of PCNN for image fusion with non-sampled contourlet transform Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology