Multivariable data imputation for the analysis of incomplete credit data

Highlights

• A novel iterative imputation method for incomplete credit data is proposed.

• The method combines an iterative mechanism and a Bayesian network classifier.

• Our method is less dependent on the hypothesis for probability distribution than other methods.

• The proposed method suits for both single variable and multivariable missing data.

• The proposed method is more accuracy and more applicable than other baseline methods.

Abstract

Missing data significantly reduce the accuracy and usability of credit scoring models, especially in multivariate missing cases. Most credit scoring models address this problem by deleting the missing instances from the dataset or imputing missing values with the mean, mode, or regression values. However, these methods often result in a significant loss of information or a bias. We proposed a novel method called BNII to impute missing values, which can be helpful for intelligent credit scoring systems. The proposed BNII algorithm consisted of two stages: the preparatory stage and the imputation stage. In the first stage, a Bayesian network with all of the attributes in the original dataset was constructed from the complete dataset so that both the network structure that implied the dependencies between variables and the parameters at each variable's conditional distributions could be learned. In the second stage, multivariables with missing values were iteratively imputed using Bayesian network models from the first stage. The algorithm was found to be monotonically convergent. The most significant advantages of the method include, it exploits the inherent probability-dependent relationship between variables, but without a specific probability distribution hypothesis, and it is suitable for multivariate missing cases. Three datasets were used for experiments: one was the real dataset from a famous P2P financial company in China, and the other two were benchmark datasets provided by UCI. The experimental results showed that BNII performed significantly better than the other well-known imputation techniques. This suggested that the proposed method can be used to improve the performance of a credit scoring system and to be extended to other expert and intelligent systems.

Introduction

For decades, credit scoring has been used by lenders as a credit risk assessment tool and an important means to reduce information asymmetry (Einav, Jenkins & Levin, 2013). In order to properly assess the borrower's ability and willingness to repay debt on time, financial institutions collect various information about borrowers from their applications and from credit bureaus, including monthly income, outstanding debt, geographical data, borrowing history, and repayment actions (Bequé & Lessmann, 2017). Using a certain expert judgment method or statistical analysis models, they then aggregated the information into a prediction of a borrower's repayment behaviors or profitability (Abdou & Pointon, 2011). In recent years, small and medium enterprises (SMSEs) have played an increasingly important role in maintaining economic growth, easing employment pressure, and facilitating people’s livelihoods (Zhang, Li & Chen, 2014). The increasing number of SMSEs has increased demand for quality credit services. At the same time, the scale of all kinds of consumer credit markets have also experienced rapid growth, which has further stimulated the demand by loan institutions for credit scoring models (Kano, Uchida, Udell & Watanabe, 2011).

Generally, three categories of credit scoring methods have been used. In the early stage, methods based on the subjective experience of credit experts, such as 5C, 5P, and LAPP, were commonly used by loan institutions (Louzada, Ara & Fernandes, 2016). Later, with the promotion of statistical techniques, regression analysis, Linear discriminant analysis (LDA; Fisher, 1936), logistical regression (LR; Sohn et al., 2016, Walker and Duncan, 1967), and Probit regression (Bliss, 1934) were introduced into credit scoring (Wiginton, 1980). An example includes the z-score model that was proposed by Altman (1968) and the risk-calc model of Moody’s. In recent years, machine learning techniques have also been introduced to credit scoring, including k-nearest neighbor (KNN; Zhou et al., 2014), support vector machine (SVM; Chen and Li, 2010, Hens and Tiwari, 2012), decision tree (DT; Kao, Chiu & Chiu, 2012), and neural network (NN; Chun‐Ling and Huang, 2011, West, 2000), and those approaches are regarded as the mainstream techniques in this field (Chen, Ribeiro & Chen, 2016). Due to this, the intelligent expert credit scoring system is widely used by credit institutions such as banks.

However, missing values are ubiquitous when conducting credit scoring on enterprises, especially for SMSEs (Gordini, 2014, Shen et al., 2009). In many applications, credit data have suffered from unavailability, scarcity, and incompleteness (Schafer, 1997). This issue significantly affects the accuracy and usability of credit scoring systems. The causes of missing data are diverse and complicated, and can include an unwillingness to respond to survey questions, data acquisition fraud, and measurement errors. Two strategies have been commonly employed in practice to overcome this challenge. One possible approach is to drop the missing instances from the original dataset, as done by Won, Kim and Bae (2012) or to perform preprocessing to replace the missing values with mean values, as done by Feng et al., 2019, Lessmann et al., 2015, and Florez-Lopez (2010). Such methods work well when the percentage of missing data is quite small and, also, when ignoring a test instance with missing values can be tolerated. However, given the scarcity of credit data, these methods are not always the best option (Schafer, 1997). They have been shown to result in the loss of information and to introduce biases into the credit scoring processes that can prevent the discovery of important credit risk factors and lead to invalid conclusions. Therefore, we mainly focused on data imputation approaches to estimate the missing values under incomplete credit data scenarios. We believe that this work will be of great benefit to improving data quality in the preprocessing process of data mining, and, consequently, to improve the performance of credit scoring models.

We presented a novel missing value imputation method that was demonstrated to be suitable for multivariable missing credit data. The proposed imputation method was inspired by the EM algorithm presented in Dempster, Laird and Rubin (1977), which was used to find the local maximum likelihood parameters of a statistical model by updating the parameters and likelihood function in an alternate iterative fashion. Combining an iterative mechanism and a Bayesian network classifier to estimate the missing values, our proposed method did the following: (1) introduced an iterative strategy that was based on increasing posterior probability to make the imputation results more fitting with the real distribution, which made the algorithm more accurate; (2) decreased the dependence on the hypothesis for probability distribution, which made the algorithm more applicable; and (3) considered all attributes in the original dataset as nodes to construct the Bayesian network in order to make the algorithm suitable for both single variable and multivariable missing data. The proposed method showed a good capability to impute missing values utilizing the entire knowledge in complete datasets, which suggested that it can be beneficial for credit scoring systems and decision makers. The proposed framework represented a significant step toward the development of robust expert and intelligent credit scoring systems.

This paper is organized as follows. in Section 2 we present a literature review of related work. Our proposed BNII algorithm for missing data imputation is described in Section 3. Experimental setting and results are given in Section 4. Finally, Section 5 provides our concluding remarks.