Abstract
This paper aims to compare the performance of four credit scoring models, namely logistic regression (LR), artificial neural network (ANN), fuzzy inference system (FIS) and adaptive neuro-fuzzy inference system (ANFIS) in predicting default probability. We use a sample of 1045 consumer credits (after oversampling the initial sample of 660 customers) granted by a Tunisian Islamic bank. The six explanatory variables retained to predict the probability of default are: residual wage, age, job tenure, profession, financing type and region of residence. Our findings reveal that ANFIS and LR have the highest discriminating power (AUC = 0.9). Regarding the type I error (false-positive) and the type II (false-negative) error, it has been proved that ANFIS has the lowest misclassification costs (MC = 0.15). The outperformance of the ANFIS comes from combining the advantages of neural networks with a fuzzy inference system. Thus, our results suggest that the ANFIS seems to be the most efficient and transparent technique for predicting credit risk in Islamic banks. Unlike ANN, the ANFIS allows bankers to justify the reasons behind the rejection of credit applications.
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Notes
Parametric methods are often robust. They are operational even when we deviate significantly from their underlying assumptions. The most crucial idea to retain is that the assumptions impact the shape of the boundary created to identify the classes in the representation area. Logistic regression, for example, produces a linear separator, even if its transfer function is non-linear, in this case, the logistic function. In contrast, it constructs a linear frontier based on a linear combination of variables to separate the positives and the negatives.
Since the sample is less than 30.
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by NA and KB. The first draft of the manuscript was written by NA and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Appendices
Appendix 1: The characteristics
The characteristics are classified into two categories: the features representing personal data and the characteristics representing bank data.
Personal details | Descriptions | Type | |
|---|---|---|---|
X1 | Age | Age is expressed in number of years | Continuous |
X2 | Marital status | Four statuses are defined: Married, Single, Divorced, Widowed | Qualitative |
X3 | Number of dependants | Expressed by the number of dependents, whether descendants or ascendants | Discrete |
X4 | Land tenure status | There are two suggestions, L for landlord (2), T for tenant (1) | Qualitative |
X5 | Occupation | Civil servant, private employee, Freelancer or retired | Qualitative |
X6 | Sex | Male or female | Qualitative |
X7 | Region of residence | Three broad residential areas have been defined: Greater Tunis, the interior regions and the Sahel region | Qualitative |
X8 | Job tenure | Calculated as the number of years in the job | Discrete |
Banking characteristics | Descriptions | Nature | |
|---|---|---|---|
X9 | Residual wage | It is the monthly pay and constitutes the salary on which the premiums are calculated | Continuous |
X10 | Credit amount | Shows the total amount of the credit | Continuous |
X11 | Financing type | These are Murabaha type products: Menzel contract, Sayara contract, Tajhizat contract, Mouchtarayet contract and Tahsinet contract | Qualitative |
X12 | Debt ratio | This is the customer’s debt ratio and indicates the payment amount in terms of gross salary. It is stated as a percentage | Continuous |
X13 | Profit rate | It is the profit rate applied by the bank, it is represented in percentage | Continuous |
X14 | Loan duration | The credit duration is given in months | Discrete |
Y | Customer status | The status is non payor = default (1), payor = non default (0) | Binary |
Appendix 2: Normality test of Shapiro–Wilk (1965)
ANFIS | FIS | LR | ANN | ||
|---|---|---|---|---|---|
Accuracy | Statistic | 0.914 | 0.888 | 0.907 | 0.93 |
df | 10 | 10 | 10 | 10 | |
Sig | 0.307 | 0.16 | 0.26 | 0.451 | |
Specificity | Statistic | 0.969 | 0.972 | 0.94 | 0.959 |
df | 10 | 10 | 10 | 10 | |
Sig | 0.882 | 0.905 | 0.548 | 0.77 | |
Recall | Statistic | 0.902 | 0.828 | 0.946 | 0.921 |
df | 10 | 10 | 10 | 10 | |
Sig | 0.23 | 0.032* | 0.627 | 0.367 | |
Precision | Statistic | 0.901 | 0.911 | 0.906 | 0.947 |
df | 10 | 10 | 10 | 10 | |
Sig | 0.226 | 0.291 | 0.256 | 0.637 | |
F1 | Statistic | 0.937 | 0.955 | 0.928 | 0.896 |
df | 10 | 10 | 10 | 10 | |
Sig | 0.52 | 0.731 | 0.431 | 0.2 | |
AUC | Statistic | 0.889 | 0.966 | 0.952 | 0.911 |
df | 10 | 10 | 10 | 10 | |
Sig | 0.164 | 0.848 | 0.691 | 0.291 | |
Appendix 3: Paired sample T-test of accuracy and specificity
Accuracy | Specificity | |||||||
|---|---|---|---|---|---|---|---|---|
ANFIS | FIS | LR | ANN | ANFIS | FIS | LR | ANN | |
Database 1 | 0.84 | 0.81 | 0.81 | 0.79 | 0.81 | 0.93 | 0.83 | 0.84 |
Database 2 | 0.88 | 0.82 | 0.84 | 0.85 | 0.86 | 0.95 | 0.87 | 0.84 |
Database 3 | 0.86 | 0.84 | 0.81 | 0.83 | 0.86 | 0.96 | 0.86 | 0.81 |
Database 4 | 0.86 | 0.83 | 0.83 | 0.81 | 0.85 | 0.93 | 0.85 | 0.84 |
Database 5 | 0.86 | 0.81 | 0.8 | 0.8 | 0.9 | 0.93 | 0.84 | 0.83 |
Database 6 | 0.82 | 0.82 | 0.83 | 0.83 | 0.87 | 0.93 | 0.83 | 0.87 |
Database 7 | 0.87 | 0.84 | 0.85 | 0.82 | 0.9 | 0.92 | 0.85 | 0.76 |
Database 8 | 0.83 | 0.8 | 0.81 | 0.81 | 0.87 | 0.93 | 0.88 | 0.89 |
Database 9 | 0.83 | 0.81 | 0.83 | 0.85 | 0.87 | 0.95 | 0.86 | 0.86 |
Database 10 | 0.86 | 0.81 | 0.8 | 0.8 | 0.89 | 0.96 | 0.86 | 0.85 |
Mean | 0.851 | 0.819 | 0.821 | 0.819 | 0.868 | 0.939 | 0.853 | 0.839 |
p-valuea | 0.000 | 0.003 | 0.006 | 0.000 | 0.124 | 0.097 | ||
p-valueb | 0.693 | 1 | 0.000 | 0.000 | ||||
p-valuec | 0.716 | 0.25 | ||||||
Appendix 4: Paired sample T-test of recall and precision
Recall | Precision | |||||||
|---|---|---|---|---|---|---|---|---|
ANFIS | FIS | LR | ANN | ANFIS | FIS | LR | ANN | |
Database 1 | 0.87 | 0.65 | 0.79 | 0.73 | 0.76 | 0.85 | 0.75 | 0.74 |
Database 2 | 0.9 | 0.64 | 0.8 | 0.86 | 0.81 | 0.89 | 0.8 | 0.78 |
Database 3 | 0.85 | 0.65 | 0.75 | 0.86 | 0.8 | 0.91 | 0.78 | 0.75 |
Database 4 | 0.86 | 0.68 | 0.8 | 0.77 | 0.79 | 0.87 | 0.78 | 0.76 |
Database 5 | 0.79 | 0.63 | 0.74 | 0.76 | 0.84 | 0.86 | 0.75 | 0.75 |
Database 6 | 0.74 | 0.65 | 0.84 | 0.78 | 0.79 | 0.86 | 0.76 | 0.8 |
Database 7 | 0.83 | 0.72 | 0.85 | 0.9 | 0.84 | 0.86 | 0.79 | 0.71 |
Database 8 | 0.77 | 0.61 | 0.71 | 0.68 | 0.79 | 0.84 | 0.79 | 0.81 |
Database 9 | 0.77 | 0.59 | 0.78 | 0.83 | 0.79 | 0.89 | 0.79 | 0.8 |
Database 10 | 0.81 | 0.56 | 0.71 | 0.73 | 0.83 | 0.91 | 0.77 | 0.76 |
Mean | 0.819 | 0.638 | 0.777 | 0.79 | 0.804 | 0.874 | 0.776 | 0.766 |
p-valuea | 0 | 0.074 | 0.234 | 0 | 0.016 | 0.034 | ||
p-valueb | 0 | 0 | 0 | 0 | ||||
p-valuec | 0.486 | 0.353 | ||||||
Appendix 5: Paired sample T-test of F1-score and AUC
F1-score | AUC | |||||||
|---|---|---|---|---|---|---|---|---|
ANFIS | FIS | LR | ANN | ANFIS | FIS | LR | ANN | |
Database 1 | 0.81 | 0.73 | 0.77 | 0.73 | 0.91 | 0.79 | 0.89 | 0.83 |
Database 2 | 0.85 | 0.74 | 0.8 | 0.82 | 0.94 | 0.79 | 0.91 | 0.9 |
Database 3 | 0.82 | 0.76 | 0.76 | 0.8 | 0.92 | 0.81 | 0.9 | 0.9 |
Database 4 | 0.83 | 0.76 | 0.79 | 0.76 | 0.93 | 0.8 | 0.9 | 0.86 |
Database 5 | 0.81 | 0.73 | 0.74 | 0.75 | 0.9 | 0.78 | 0.88 | 0.87 |
Database 6 | 0.77 | 0.74 | 0.8 | 0.79 | 0.83 | 0.79 | 0.9 | 0.87 |
Database 7 | 0.84 | 0.78 | 0.82 | 0.8 | 0.91 | 0.82 | 0.91 | 0.87 |
Database 8 | 0.78 | 0.71 | 0.75 | 0.74 | 0.89 | 0.77 | 0.91 | 0.83 |
Database 9 | 0.78 | 0.71 | 0.79 | 0.81 | 0.91 | 0.77 | 0.92 | 0.91 |
Database 10 | 0.82 | 0.7 | 0.74 | 0.74 | 0.88 | 0.76 | 0.89 | 0.86 |
Mean | 0.811 | 0.736 | 0.776 | 0.774 | 0.902 | 0.788 | 0.901 | 0.87 |
p-valuea | 0 | 0.011 | 0.014 | 0 | 0.92 | 0.018 | ||
p-valueb | 0 | 0.005 | 0 | 0 | ||||
p-valuec | 0.25 | 0.004 | ||||||
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Ayed, N., Bougatef, K. Performance Assessment of Logistic Regression (LR), Artificial Neural Network (ANN), Fuzzy Inference System (FIS) and Adaptive Neuro-Fuzzy System (ANFIS) in Predicting Default Probability: The Case of a Tunisian Islamic Bank. Comput Econ (2023). https://doi.org/10.1007/s10614-023-10496-y
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DOI: https://doi.org/10.1007/s10614-023-10496-y