An empirical application of a hybrid ANFIS model to predict household over-indebtedness

Abstract

The increase in debt levels of families in different parts of the world has drawn the attention of organizations dedicated to the prevention of financial risk and has highlighted the need to develop early detection methods for over-indebtedness. In this paper, we propose a hybrid model of the adaptive neural fuzzy inference system (ANFIS) and Probit model for the prediction of household over-indebtedness. The proposed model is compared with Probit, artificial neural networks (ANN), classification and regression trees (CART), random forest (RF) and support vector machine (SVM) models. The most relevant parameters for the performance of each model are optimized, and we address data balance problems through the synthetic minority over-sampling technique (SMOTE). We use data obtained from the Financial Household Survey of the Central Bank of Chile. The results show that the proposed model performs significantly better than the reference models in terms of the correct classification of indebted individuals. Consequently, this model provides an innovative understanding of household over-indebtedness, which can be useful for different governmental entities focused on preventing excessive indebtedness and maintaining financial stability.

Appendices

Appendix 1

1.1 Variable description

The following table describes the variables used in this study to describe household financial over-indebtedness for the developed models.

Variables	Description
${X}_{1}$ Gender	Dichotomous variable that describes the gender of the head of household where:1: Woman / 0: Man
${X}_{2}$ Age	Integer variable that indicates the age of the head of household
${X}_{3}$ Savings	Continuous variable that describes the total declared amount of savings recorded by the household in the last 12 months. Expressed in millions of Chilean pesos
${X}_{4}$ Workers	Integer variable that describes the number of members of the household that are working
${X}_{5}$ Card	Dichotomous variable that indicates if any members of the household have a credit card with:1: Has a card/ 0: Does not have a card
${X}_{6}$ Marital status	Dichotomous variable that represents the marital status of the head of household with:1: Married or partner / 0: Other
${X}_{7}$ Income	Continuous variable that indicates the total amount of income that the household receives monthly. Expressed in millions of Chilean pesos
${X}_{8}$ Educational level	Integer variable that represents the years of schooling of the head of household. Chile's educational system has an average of 8 years for primary education, 4 years for secondary education, and 6 for higher education. The survey also considers postgraduate studies or second professions
${X}_{9}$ Mortgage burden	Continuous variable that indicates the total amount that the household pays monthly for mortgage debt. Expressed in millions of Chilean pesos
${X}_{10}$ Educational debt	Continuous variable which indicates the total amount owed by the household for the education of its members. Expressed in millions of Chilean pesos

Appendix 2

1.1 Performance measurement

To evaluate and compare all the models, we use the confusion matrices obtained from each evaluated model and calculate the accuracy metrics (ACC), positive ($A{R}_{P}$) and negative $(A{R}_{N})$ class accuracy and area under curve (AUC). These are defined in Table

Table 6 Confusion matrix and accuracy measure confusion matrix

6 as follows:

$$\mathrm{Accuracy }\left(ACC\right)= \frac{TP+TN}{TP+FP+TN+FN}$$

(1)

$$\mathrm{Positive class accuracy} \left(A{R}_{P}\right)=\frac{TP}{TP+FN}$$

(2)

$$\mathrm{Negative class accuracy }\left(A{R}_{N}\right)=\frac{TN}{TN+FP}$$

(3)

$$\mathrm{Area under Curve }\left(AUC\right)=\frac{A{R}_{P}+A{R}_{N}}{2}$$

(4)

In order to supplement the evaluation of over-indebtedness model performance, we consider the presence and significance of misclassification. Given a null hypothesis (over-indebted household), each time this hypothesis is rejected when it is true, a type I error is committed. On the other hand, when the null hypothesis is false (household is not over-indebted) and it is rejected, a type II error is committed. For the over-indebtedness models developed in this article, the relevance of a type I error is much greater than a type II error, since it impairs the usefulness and general applicability of the model. For this reason, the key performance measurement is the AUC.