# Research on PPP Enterprise Credit Dynamic Prediction Model
## 2 Materials and Methods
### Data Processing and Characteristic Derivative Analysis
#### 2.2.1 Multivariate Joint Distribution Analysis  
\(\rho_{\text{LGFVs}}\) (Spearman's rank correlation coefficient) is an indicator of the correlation between two variables. In this paper, the confusion matrix of 26 rating indicators is calculated using the Spearman analysis method, and the variables with correlation coefficient greater than 0.8 are retained [19], and their IV values are retained as the input variables.  
As shown in Formula (1). Among them, \(x_{\text{\tiny{eff}}}\) represents the rank value of the Variable 1, and \(y_{\text{\tiny{vi}}}\) represents the rank value of the Variable 2, \(n\) is the numbers of samples, \(\rho_{LGFVs}\) is the correlation coefficient between the rank variables.  
\[\rho_{LGFVs}=1-\frac{6\sum{(x_{\text{\tiny{gi}}}-y_{\text{\tiny{vi}}})^{2}}}{ n(n^{2}-1)} \tag{1}\]  
Since the dataset samples do not obey the normal distribution law, in order to objectively predict the credit rating of LGFVs based on the machine learning model, it is necessary to use the Spearman analysis method to construct a correlation coefficient greater than 0.8 credit qualification, influence coefficient matrix, and calculate the correlation coefficient between the two indicators [20]. A total of 11 pairs of variables with indicators greater than 0.8 were obtained, as shown in Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable 1 (x\({}_{\text{\tiny{pri}}}\))** & **Variable 2 (y\({}_{\text{\tiny{gi}}}\))** & **Correlation Coefficient** \\ \hline Net worth & Total assets & 0.9368 \\ Return on equity & Assets net profit margin & 0.9165 \\ Operating profit/Total assets & Assets net profit margin & 0.8540 \\ Asset-liability ratio & Equity ratio & 0.9924 \\ Total assets turnover & Current assets turnover & 0.8287 \\ Tax Revenue & The public finance budget revenues & 0.8219 \\ The local GDP & The public finance budget revenues & 0.8523 \\ Tax Revenue & 0.9934 \\  & The public finance budget revenues & 0.8019 \\ GDP per capita & Tax Revenue & 0.8536 \\  & The local GDP & 0.8631 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristic variables correlation analysis.  
Joint distribution can establish a pairwise comparison matrix by a heterogeneous group of factors in a multi-dimensional problem event, identifying key points based on a matrix plot. The strength performance of the correlation coefficients based on Table 2 was theoretically examined using the measure in [21]. The goodness of fit of the combined values of the various indicator variables was examined by plotting multi-variate joint distribution plots in Python for a total of seven groups of variables: Net worth, Total assets, Equity ratio, Asset-liability ratio, The public finance budget revenues, Tax revenue, and GDP per capita. As shown in Figure 2.  
It can be seen that the sample scatter points corresponding to the seven groups of functions are well distributed. However, we observe the diagonal sample distribution and find that Asset-liability ratio, The public budget revenues, Tax revenue, and The local GDP have a large area of default sample distribution.  
Figure 2: Multivariate joint distribution.  
Among them, the asset-liability ratio is the most widely distributed variable among default samples. The higher the Asset-liability ratio, the higher the probability of default samples. Due to the limited liability effect of debt, firms with higher debt levels are more aggressive and have higher debt risk [22]. This shows that LGFVs should improve financial management and financial planning, prevent debt default risk, and improve credit evaluation levels.