(CW) of a corporate entity or individual
is determined by using different credit scoring models. Hence,
a high credit score results in a high creditworthiness, this
score is determined on the basis of the wide customer database
created generally by banks over the years [1]. It is not possible
that all customers will act the same way when it comes to
financial performance, therefore, banks need to know their
good or bad customers, and they will need credit scoring (CS)
system to do so [2]. Article [3], defined CS as the means of
analyzing the likelihood of applicant to falter in their
repayments, or not in order to avoid financial losses. It is
important to collect information from bank customers and
other financial institutions to manage the credit risks, and at
the same time, to reach an important decision to lend some
money to their clients or not. In other words, this process can
help to separate good borrowers from bad ones. This means
that some borrowers have clean and good records; therefore,
banks can classify them as “good borrowers”. A few others,
not having such good records, can be considered as “bad
borrowers”. It is worth noting that such simple selection
process may not guarantee a correct classification. Hence, new
accurate automated systems reducing the prediction errors are
urgently needed in order to handle large and complex CS
datasets [4]. To deal with this challenge, IT systems have
become very popular among scientists and institutions in the
last several years. Over the past decades, several scientific
studies have attempted to assess the credit scoring potential of
bank customers using different predictive models [5]. A large
number of data mining (DM) and machine learning (ML)
techniques have been used for this purpose, including, support
vector machines (SVMs), neural network (NNs), decision
trees (DTs), logistic regression, fuzzy systems, etc. Each of
these studies analyzed different data sets to show the
effectiveness of their methods. In general, finding a
relationship between low and high credit risks is one of the
most popular research areas in the field of financial
forecasting, consisting of developing new predictive systems.
As to the main contribution and novelty of this work, we
introduce a new method for predicting financial distress
related to credit applicants called splitting the learning set into
two regions (SLS2Rs). The goal of our proposed method
consists on the construction of two regions from a learning
set, the first named "Solvency Region" that contains the
feature vectors of the elements, which are settled their credits
in term and the second one named "Non-Solvency Region",
which contains the feature vectors of the elements who failed
in the payment of their credits. Therefore, to predict the risk of
a customer default, it is enough to know which of the both
regions include his feature vectors; if it doesn’t correspond to
any region, the credit decision making requires so more
analysis. To evaluate the performance and to demonstrate the
effectiveness of our method, a series of experimental tests and
Creditworthiness
1. Introduction
A new machine learning method for bank credit risk analysis
ZAYNAB HJOUJI, MOHAMED M’HAMDI
Sidi Mohamed Ben Abdellah University, BP 42, Fez 30000
MOROCCO
Abstract—We present in this article a new approach to predict the creditworthiness of borrowers that we call
“Method of separating the learning set into two regions”. The goal of this approach is to build two regions from
a training set. Thus, to predict the solvency of borrowers, it suffices to identify which of the two regions has its
characteristic vectors; if it does not correspond to any region, credit decision-making requires further analysis.
To test our approach, a large set of real and recent credit data obtained from the UCI repository is used, we
trained also on a real credit database of a Moroccan bank and the creditworthiness of borrowers is analyzed at
using two performance measurement indicators such as classification accuracy and AUC of the ROC curve as
a robustness measurement criterion. The proposed model was compared with three traditional machine learning
algorithms: LR, RBF-NN and MLP-NN. The experimental results show the superiority of the proposed
approach.
Keywords— Artificial Intelligence, Systems Theory, Machine Learning, Credit risk prediction.
Received: June 25, 2021. Revised: March 19, 2022. Accepted: April 23, 2022. Published: May 20, 2022.
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a comparative study are applied. The obtained results suggest
that the proposed methodology is very promising in the bank
credit risk prediction field and it could be applied to any other
CS dataset as well.
Credit scoring (CS) model have been developed by banks and
researchers to improve the process of assessing credit
worthiness during the credit evaluation process. In this
section, we will review some widely used techniques for
predictive credit scoring applied in detecting credit worthiness
borrowers in order to create a baseline for the selection of an
appropriate tool for developing a banking creditworthiness
prediction models, note that this study only reviews the most
commonly used techniques as it would be almost impossible
to look at all techniques applied in credit scoring. Typically,
the existing literature surveys on creditworthiness borrowers
prediction or credit scoring models shows that most of these
models are either statistical [6] or artificial intelligence (AI)
[7] based methods.
A credit scoring solution can be built using Metrological
statistics or statistical models, including; Multiple
Discriminant Analysis (MDA)[8], Logistic Regression (LR)
[8]-[9], Bayesian approach[10]-[11], Probit analysis[12],
Multiple regression and more others. These models have been
proven to be quite effective, however, for solving relatively
less complex problems in prediction credit risk fields. Some of
these techniques are widely applied for prediction and
diagnosis in the banking credit risk assessment literature,
notably; Multiple Discriminant Analysis and Logistic
Regression tools[13]. MDA instrument was initially applied
by[14] to analyze the financial distress, bankruptcy and
default risks. However, the use of this method has frequently
been criticized because of its assumption of the categorical
nature of credit data and the fact that the covariance matrices
of good and bad credit are unexpected to be equal [15], [16].
In parallel with the MDA approach, LR instrument is
becoming a common alternative for making credit-scoring
models. Fundamentally, it was emerged as the better technique
of choice in anticipating dichotomous outcomes. It has been
concluded as one of the most appropriate techniques in the
credit risk assessment literature. Authors in article [17]
stressed that logistic regression algorithms perform best
among all statistical credit risk assessment algorithms. In this
context, several studies has shown the effectiveness of the
logistic regression approach versus the LDA approach in
detection of credit worthiness borrowers. As this model is
widely used, a large number of its application have been
reported in literature[18].
Against lot of statistical methods and in order to improve
prediction performance for detection banking (CW)
borrowers, artificial intelligence and soft computing
techniques have emerged. In fact, overall the main AI method
for prediction (CW) are Artificial Neural Networks (ANNs)
[19-20], Support Vector Machines (SVMs) [20]-[21], Fuzzy
Logic (Fuzzy) [21], Decision Tree(DT)[22], K-Nearest
Neighbor (K-NN)[23], Random Forests algorithms(RFs) [24],
Genetic Algorithm [25]-[26], and more others.
AI tools are computer-based techniques of which Artificial
Neural Network (ANN or NN) is the most common for
bankruptcy prediction simply because it have shown a greater
correctness of predictability than any others techniques in
(CW) models prediction or credit scoring models, due to its
associated memory characteristic and generalization
capability, flexibility, robustness, and higher classification
accuracy [27]. Many studies arbitrarily employed neural
networks algorithms for modelling credit risk compared to
others methods of (CW) prediction models [13], [28]. In their
study [29], compares Bayesian networks (NB) with Artificial
Neural Network (ANNs) algorithm based on back propagation
for predicting recovered value in a credit operation. They
finds that both the ANN and the NB models provide reliable
outcomes, but the ANN is more effective for predicting credit
risk with an average score of 82%. Further, Authors in article
[30], explore a new practical way based on the Neural
Networks that would help the banker to predict the non-
payment risk the companies asking for a loan. To evaluate the
performance of their technique, they compare it with those of
discriminant analysis, using a correlation test in a sample of
86 Tunisian companies and 15 financial ratios over the period
from 2005 to 2007. The results shows that the neural networks
techniques is more accurate in term of predictability. In the
same sphere of predicting CW , a research conducted in [31]
suggests an ensemble techniques bagging with neural network
for creditworthiness assessment. By using four measurement
criteria such as Accuracy, Specificity, Sensitivity and the
AUC of the ROC curve, the proposed model showed
promising results and outperforms other models for Bosnian
commercial bank dataset and feature selected datasets and also
for two real-world credit datasets German and Australian.
Authors demonstrate that the proposed model is empirically
proven to be suitable for further use in the assessment of the
creditworthiness of applicants.
In the same context, Lin et al [32] discussed in their work the
application of the classification function and artificial neural
networks such as (MLP) and (RBF) in identifying the risk
categories of the studied firms. The results showed that the
application of the artificial neural network and classification
function can effectively support the credit evaluation of
applicants. In their study, authors in [33] examined the credit
decision using logistic regression and neural network (RBF).
The results showed that the logistic regression model was
superior to the radial basis function (RBF) model in terms of
overall accuracy rate. However, the radial basis function was
better than the identification of likely defaulters. Recently, the
work of Yiping. G [34] present a credit risk assessment
algorithm based on BP neural network, and the simulation
results showed that, compared with the traditional LR
algorithm, the proposed model has higher classification
accuracy and can effectively reduce investors' risk.
2. Creditworthiness Banking Detection
Models: a Brief Review of Literature
2.1 Statistical Models for
Detection of Creditworthiness
2.2 Artificial Intelligence Models
for Detection of Creditworthiness
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This model typically requires a quantity of data, which is
accumulated by the bank to form a larger learning set to
achieve performance gains through predictions; this set can be
divided into two categories. The learning set consists of the
bank's credit customers, which can be classified into two
groups with reference to the opinion of the bank's credit
manager: the set of successful customers is the category
containing all the cases that managed to repay their credit on
time i.e. they are considered as solvency customers; each
element of this category is denoted by 0 (Table 1 in blue) and
the set of unsuccessful customers is the set of elements that
failed to recover their credit i.e., they are considered as non-
solvency customers, each element of this set is denoted by 1
(Table 1 in grey).
Table 1.The repartition of the studied categories.
1
1
1
0
0
0
Classe1: The group, which contains S Solvency/successful
customers (matrix in gray). The centroid of this class is:
s
i
pi
i
i
i
s
ii
x
x
x
x
s
X
s
c
1
3
2
1
1
0
11
(1)
Classe2: The group that contains non-Solvency / non-
successful customers (matrix in blue).. The centroid of this
class is:
N
i
pi
i
i
i
SN
N
Si i
x
x
x
x
X
SN
C
1
3
2
1
1
1
1
1
(2)
The worst element among successful customers is the element
, which is furthest from the centroid of this class (see
Fig.4). Therefore is defined as:
000 ,...,1),,(max),( rSiXCdXCd iw
(3)
The best element among non-successful customers is the
element furthest from the centroid of this class. Therefore
is defined as:
111 ,...,1),,(max),( rNSiXCdXCd ib
(4)
Where is the Euclidean distance defined by :
P
iii yyYYd
1
2
2121 )(),(
(5)
We constitute the following two regions: the ball with center
and radius
000000 ),(/),( rXCdRXrCR N
(6)
Fig.1.The region
),( 000 rCR
with center and radius
And the region with center and radius
11111 ),(/),( rXCdRXrCR N
(7)
Fig.2. The region
),( 111 rCR
with center and radius .
1) The set of feature vectors of successful
customers is completely included in the region
),( 000 rCR
,i.e.
),(,,1, 000 rCRSiXi
(8)
2) The set of feature vectors of non-
successful customers is completely included in the
region
),( 111 rCR
,i.e.
),(,,1, 111 rCRNSiXi
(9)
Proof:
1) According to equation (6), to show that a vector
belongs to the region , it is enough to show that
3. Development of the Proposed Model
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From the equation (3), is the distance that
maximizes the set of distances between and the feature
vectors of successful companies It’s means
that;
000 ),(),( rXCdXCd wi
for all i = ,…,S (10)
Therefore,
),(,,1, 000 rCRSiXi
2) In the same procedure of remark 1, according to
equation (4),
),( 1b
XCd
the distance that maximizes the
set of distances between
1
C
and the feature vectors of
non-successful clients
.,,1, NSiXi
This means
that:
111 ),(),( rXCdXCd bi
for all
NSi ,,1
(11)
Therefore,
),(,,1, 111 rCRNSiXi
Points ● represent the feature vectors
successful customers.
Points ● represent the feature vectors
of non-successful
customers.
Region .
Point ● represents the centroid
of the class 0
Point ● represents the centroid
of the class 1
Point ● Represents the worst
element among successful customers.
Point ● Represents the best
element among non-successful
customers.
Region
Fig.3. The distribution of the learning set
NiXi,,1,
into two b.
(a): separable learning set
(b): non-separable learning set
Fig.4. Representation of learning sets.
In summation, using the previous important remarks, we
deduce the procedure followed to predict the bank credit risk
of a customer based on a precise learning set accumulated by
the bank. We proceed so with the following phases:
Phase of splitting the learning set into two regions:
This phase allows to build two spherical zones by splitting the
learning set into two regions
),( 111 rCR
and
),( 000 rCR
the
first contains the risky elements and the second contains the
non-risky elements. Depending on the nature of the set under
consideration, we follow one of the following two cases :
Case 1: If the learning set, is separable (Fig. 4 (a)), we follow
the following steps:
- Step 1: We calculate the barycentre of all
Successful customers.
- Step 2: We calculate the barycentre of all non-
Successful customers.
- Step 3: We determine the worst element among
the Successful customers and the radius
- Step 4: We determine the best element among non-
Successful customers and the radius .
Case 2: If the learning set is non-separable (Fig.4 (b)), in this
case, to build the two regions we can use the following new
optimization problem:
Find
w
X
and
b
X
such that:
NSjSiXCdXCdXCdXCd jibw ,,1;,,1),,(),(max),(),( 1010
Under constraint
),(),( 111000 rCRrCR
(12)
i.e.
Find
w
X
and
b
X
such that:
NSjSiXCdXCdXCdXCd jibw ,,1;,,1),,(),(max),(),( 1010
Under constraint
),(),(),( 1010 CCdXCdXCd bw
(13)
Remark: In any case, we can separate the database used into
two regions
),( 000 rCR
and
),( 111 rCR
such as
.),(),( 111000
rCRrCR
Phase of prediction CW / credit risk for new customer:
Step 1: Feature vector extraction
p
x
x
x
X
2
1
of customers.
Step 2: We calculate the distances
),( 0XCd
and
),( 1XCd
.
Step 3: Verify that:
- If
),(,),( 00000 rCRXrXCd
, it means that
there is no risk, the customer’s application is
strongly accepted.
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- If
11 ),( rXCd
and
00 ),( rXCd
, we will compare
),( 1XCd
and
),( 0XCd
, so:
If
),(),( 01 XCdXCd
, the credit application
is weakly rejected.
If
),(),( 10 XCdXCd
, the credit application
is weakly accepted.
It should be noted that whether the credit application is
rejected or weakly accepted means that the decision is made at
the discretion of the bank manager.
In this section, we will describe the bank credit databases on
the basis of which we will apply and implement our proposed
method (An international and a Moroccan credit database)
methods.
For this work, we use three real life credit datasets (obtained
from South German, Australia, and Taiwan banks) of which
are publicly available from the UCI machine-learning
repository [35]. We decided to use those three credit datasets
because they are very frequently used in the credit-scoring
field especially to test the performance of the classification
model, which conveniently allows us to use them to test the
classification performance of the proposed model and
compare the results to other reference models.
Moroccan dataset is provided by one of the commercial banks
in Morocco. This customer credit application dataset is used in
experiments. It consist of 1000 examples, of which 788
observations (78, 8%) are classified as creditworthy
borrowers, while 212 observations (21, 2%) are classified as
non-creditworthy borrowers and 14 predictive features. This
search used a dichotomous variable – Non-creditworthiness
– (Yes = 1, No = 0), as the outcome variable.
The classification goal is to predict the non-creditworthiness
of borrowers:
Dependent Variable: Creditworthiness borrowers
0 = Creditworthy borrowers.
1= Non-Creditworthy borrowers.
In order to evaluate the performance of creditworthiness
prediction models, various performance evaluation criteria can
be used such as the classification accuracy, Recall or
Sensitivity, Prediction rate, False Alarm rate, Specificity,
AUC of the ROC curve, the F-measure, the Kolmogorov-
Smirnov test, Gini- Coefficient, and among others.
Performance evaluation criteria used in this empirical study
are Classification accuracy, the AUC of the ROC curve with
adding the box plots of predicted pseudo-probabilities as a
powerful metric.
- The AUC value of the ROC curve:
The ROC curve (Receiver Operating Characteristic) is a
useful tool for evaluating the effectiveness of methods and
viewing their capabilities, particularly in the field of credit
risk assessment.
- The Classification Accuracy rate :
The classification accuracy is defined as
Accuracy (%) =
100% ×
NCT
NCCC
(14)
Where, NCCC is the number of correctly classified cases and
NCT is the number of cases used in the test.
In this section, we will discuss the methodology of
implementing the proposed model using some measurement
criteria such as presented in (subsection C), in order to
evaluate the performance of our proposed model with each
compared methods by reporting the results of implementing
our predictive proposed method on each International and
Moroccan data sets. This section is divided into two sections
International credit datasets results and Moroccan credit
datasets results.
Implementation Process for Comparative Analysis
We test the performance of our approach based on splitting
the learning set into two regions one is risky and the other is
not risky, we worked on three real life datasets (South
German, Australia and Taiwan). This real life datasets
classifies credit applicants described by a set of attributes as
good or bad credit risks, has been successfully used for credit
scoring and evaluation systems in many previous works.
Thereafter, we divide each database into two sets, one for the
learning set and the other for the model validation set.
The validation set is also divided into five sub-sets of testing
data S1, S2,..., S5. We then provide a comparative study of
the performance of our predictive proposed model and other
well-known and widely used models in the field of
creditworthiness borrower’s prediction, such as Logistic
Regression (LR), Radial Basis Function Neural Networks
(RBF-NN), and Multilayer-Perceptron Neural Networks
(MLP-NN) as two robust neural network functions in the area
of credit risk prediction.
To measure the predictive ability of each method, we selected
the classification accuracy rate as an appropriate and a
powerful metric used in predicting creditworthiness of
borrowers.
It should be pointed out that, all our numerical experiments
are performed in Matlab 2017 on a PC HP, Intel(R) Core(TM)
I5-5200U CPU @ 2.20 GHz, 4GB of RAM, O.S w.7.
4. Data Collection and Variable Definition
4.1 International Bank Credit Datasets Description
4.2 Moroccan Bank Credit Datasets Description
4.3 Performance Metrics / Measurement Criterion
5. Experiment Results and Analysis
5.1 Experimental Tests and Comparative
Study on International Banks
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Tables 2, 3 and 4 show the results of predicting borrowers
creditworthiness for the three databases. From these results,
we can see that our predictive proposed method based on
splitting the learning set into two regions outperformed the
tested methods for all the five tested sub-datasets.
Table 2. Comparison of the 4 methods of creditworthiness
prediction results using South German for the tested sets S1,
S2, S3 and S4.
Method
S1
S2
S3
S4
S5
LR
98.71%
93.19%
90.11%
79.12%
75.22%
RBF
99.63%
94.07%
90.77%
81.08%
76.33%
MLP
99.81%
94.43%
91.85%
83.12%
78.42%
Proposed
100%
96.84%
94.73%
91.54%
89.11%
Table 3. Comparison of the 4 methods of creditworthiness
prediction results using Australia Credit datasets.
Method
S1
S2
S3
S4
S5
LR
95.60%
90.18%
87.00%
76.01%
69.93%
RBF
96.52%
90.85%
87.66%
79.21%
73.22%
MLP
96.70%
91.32%
88.74%
80.01%
75.31%
Proposed
99.65%
98.67%
94.62%
91.43%
89.02%
Table 4. Comparison of the 4 methods of creditworthiness
prediction results using Taiwan Credit datasets.
Method
S1
S2
S3
S4
S5
LR
93.45%
88.36%
81.48%
71.61%
69.89%
RBF
94.63%
91.11%
88.07%
77.12%
70.47%
MLP
95.55%
90.96%
86.61%
80.42%
75.12%
Proposed
99.71%
98.72%
95.03%
90.98%
89.44%
Implementation Process for Comparative Analysis
To prove the practicability and the higher performance of our
predictive proposed approach of which its consists on splitting
of the learning set into two regions, a comparative analysis
with some widely and commonly used methods for
creditworthiness prediction models such as Artificial Neural
Networks, including Multilayer-Perceptron network (MLP),
Radial Basis Function (RBF) and Logistic Regression (LR) is
performed and presented in this section.
Prediction by RBF neural network model
The RBF classification results by partition and overall are
presented in Table 5. As shown, the RBF network correctly
classified 578 out of 694 clients in the training sample and
238 out of 306 clients in the test sample. Overall, 83.3% of
training cases and 77.8% of test cases were correctly
classified.
Table 5. RBF-NN classification.
Sample
Observed
Predicted
NO
YES
Correct
Training
NO
529
23
95,8%
YES
93
49
34,5%
Overall
89,6%
10,4%
83,3%
Testing
NO
220
16
93,2%
YES
52
18
25,7%
Overall
88,9%
11,1%
77,8%
The box plots of the predicted pseudo-probabilities are
displayed in Fig.5. For the dependent variable outcome of
customer classification, the chart displays boxplots that
categorize the predicted pseudo-probabilities based on whole
the data set. The 1st boxplot, starting from the left, shows the
predicted probability of the observed creditworthy customer
being in the "Non-defaulting Customer" category. The 2nd
boxplot shows the probability of a creditworthy customer
being classified as a "Non-defaulting customer" when it was
actually in the "Defaulting customer" category. The 3rd
boxplot shows, for outcomes that observed the ''Defaulting
Customer'' category, the predicted probability of the ''Non-
defaulting Customer'' category. The right boxplot shows the
probability of a customer being reported in default when it is
actually classified in the correct ''Defaulting Customer''
category.
Fig.5. Predicted-by-observed chart for RBF-NN.
The ROC curve of the RBF network prediction method based
on the combined training and test samples is presented in
Fig.6. As can be seen the method performed better in terms of
its ROC curve.
Prediction by MLP neural network model
The classification findings for the MLP-NN model by
partition and overall are reported in Table 6. As shown, the
MLP network correctly classified 579 out of 694 clients in the
training sample and 245 out of 306 clients in the test sample.
Overall, 83.4% of training cases and 80.1% of test cases were
correctly classified.
International credit datasets results
5.2 Experimental Tests and Comparative
Study on Moroccan Bank
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Fig.6. ROC curve for RBF-NN method.
Table 6. MLP-NN classification
Sample
Observed
Predicted
NO
YES
Percent
correct
Training
NO
519
33
94,0%
YES
82
60
42,3%
Overall %
86,6%
13,4%
83,4%
Testing
NO
217
19
91,9%
YES
42
28
40,0%
Overall %
84,6%
15,4%
80,1%
Fig.7. shows box plots of predicted pseudo-probabilities. For
the dependent variable customer classification outcome, the
chart displays box plots that classify the predicted pseudo-
probabilities based on the whole dataset. The 1st from the left,
boxplot shows the predicted probability of the observed
creditworthy customer to be in the ''Non-defaulting
customer'' category. The 2nd boxplot shows, the probability
for a creditworthy customer to be classified in ''Non-
defaulting customer'' category although he really was in ''
Defaulting customer'' category. The 3rd boxplot shows, for
outcomes that have observed category ''Defaulting customer''
the predicted probability of ''Non-defaulting customer''
category. The right boxplot shows, the probability a customer
is declared defaulted who really be classified in the right
category of '' Defaulting customer''.
Fig.7. Predicted-by-observed chart for MLP-NN.
The ROC curve of the MLP network predictive model based
on both training and test samples together is shown in Fig.10.
It can be observed that the model performed better in terms of
ROC curve. If a customer in the category '' Defaulting
customer '' and a customer in the category '' Non defaulting
customer '' are randomly selected, there is 0.744 probability
that the pseudo-probability predicted by the model for the first
customer to be in the '' Non defaulting customer '' category is
greater than the pseudo-probability predicted by the model for
the second client to be in the '' Non defaulting customer ''
category.
Fig.8. ROC curve for MLP-NN method
Prediction by Regression Logistic model
The current study utilized 694 cases to build the logistic
Regression-Scoring model and 306 cases to assess the
developed model. The chi-square result testing the
significance of the LR model is presented in Table 14. It
provides statistical evidence that there is a relationship
between the selected variables and the dependent variable. It
shows that the chi-square probability (144.989) is less than
0.05. In additional, the classification ability of the LR model is
summarized in Table 7. The correct and right predictions are
reported in the diagonal cells, while the off-diagonal cells
contain the wrong and incorrect predictions. It is noticeable
that 87.1% of the non-defaulting clients were classified
correctly, 33.3% of the defaulting clients were classified
correctly, and overall, the correct classification rate of the LR
model was 78% with a threshold of 0.5.
Table 7. Logistic Regression classification results.
Observed
Predicted
Training
cases
Testing
cases
No
Yes
correct
No
Yes
correct
No
500
74
87,1%
196
40
83,1%
Yes
80
40
33,3%
20
50
71,4%
Overall
78%
80,4%
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Furthermore, the developed method was tested using a testing
subset of 306 cases which of (236 No defaulting clients and
70 defaulting clients) that was not used to create the model.
The overall classification rate for the testing sample was
80,4%. In fact, the LR credit-scoring model performed better
when classifying No-defaulting clients (83,1%) than
classifying defaulting clients (71,4%). Similarly, to evaluate
the performance of the logistic regression model, we choose
the ROC curve of this model based on the combined learning
and testing samples illustrated in Fig.9. below. We can
observe that the model performed better in terms of the ROC
curve.
Fig.9. ROC curve for LR model.
Prediction by our predictive proposed method
By using, the same learning and testing sample applied in the
assessment of the three-credit risk prediction methods on our
proposed predictive method, we achieved the following
findings:
Table 8. Our predictive proposed method summary.
Training
Cross Entropy Error
286,684
Incorrect Predictions
16,5%
Stopping Rule Used
1 consecutive step(s) with no
decrease in error
Training Time
0:00:00,59
Testing
Cross Entropy Error
128,636
Incorrect Predictions
15,6%
Our predictive proposed method summary, presented in Table
8, contains information about the results of the training and
testing sample in which the percentage of incorrect prediction
in the training set was 16.5% and for the testing set was only
15.6%, or the least percentage of incorrect prediction of the
other methods evaluated. In fact, the small value (= 128.636)
of the cross-entropy error in the test sample signals the
robustness of our predictive proposed method in predicting
creditworthiness of borrowers.
As Table 9 illustrates, our predictive proposed method
correctly classified 579 out of 694 clients in the training
sample and 261 out of 306 clients in the test sample. Overall,
83.4% of training cases and 85.3% of test cases were correctly
classified.
Table 9. Our predictive proposed method classification
results.
Sample
Observed
Predicted
NO
YES
correct
Training
NO
499
30
94,3%
YES
85
80
48,5%
Overall
84,1%
15,9%
83,4%
Testing
NO
240
19
92,7%
YES
26
21
44,7%
Overall
86,9%
13,1%
85,3%
As observed in the ROC plot presented in Fig.10. Our
predictive proposed method performed statistically better than
other credit risk assessment methods.
Fig. 10. ROC curve for the predictive proposed method.
Table 10. The summary table of the results of the compared
methods.
Methods
Overall accuracy
AUC value
RBF-NN
77,8%
0,712
MLP-NN
80,1%
0,744
LR
80,4%
0,755
proposed method
85,3%
0,809
From the comparison analysis of predictive capability
conducted on the four creditworthiness borrowers prediction
methods, it is apparent that our proposed predictive method
provided better results in terms of predicting creditworthiness
as it is illustrated in Table 10. In fact, our predictive proposed
method correctly classified 85.3% of the tested cases, which is
better than the Radial Basis Function (77.8%), the Multilayer
Perceptron (80.1%), and the Logistic Regression method
(80.4%). Therefore, our proposed method is more accurate
than other credit risk assessment methods. Hence, Fig.11
shows the ROC curves of the classification models tested in
this study. One can see that our predictive proposed method
achieved better performance in terms of ROC curve (orange
curve) compared to the three others methods within our
dataset. We conclude that the proposed method obtained the
best performance on our Moroccan dataset.
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Fig.11. ROC curves obtained by the different compared
methods.
To summarize, we proposed a method for predicting
creditworthiness of borrowers, which we have called the
method of splitting the learning set into two regions, one risky
and one not risky. Three contemporary machine-learning
methods were compared, to identify the most efficient and
best performing model. After giving a description of the using
International and Moroccan datasets on the basis of which we
have applied our predictive proposed method, each model was
compared on the basis of two performance evaluation metrics:
Classification Accuracy and the AUC value of the ROC curve.
As observed in the experimental results, the ROC plot of the
proposed method is classifier performed statistically better
than other classifiers compared methods which is proven by it
AUC value which is equal to 0,809 and an accuracy of 85,3%.
Based on the test results, it was concluded that our proposed
method based on the splitting the learning set into two regions
is the most favorable classification model since it gives the
highest accuracy in forecasting and best performance in
identification of creditworthiness of borrowers.
The authors of the essay express their sincere gratitude to the
editor and other reviewers and acknowledge their valuable
comments and contributions.
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Zaynab Hjouji carried out the Simulation and Statistics of the
empirical study.
Mohamed M’hamdi was responsible for the planning of the
article.
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2022.21.12
Zaynab Hjouji, Mohamed Mhamdi
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117
Volume 21, 2022
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