Applicability and effectiveness of classifications ...

Applicability and effectiveness of classifications models for achieving the twin objectives of growth and outreach of microfinance institutions Manojit Chattopadhyaya, Subrata Kumar Mitrab a,b Information Technology Area, Indian Institute of Management Raipur, GEC Campus, Sejbahar, Raipur 492015, India

ABSTRACT Measuring performance of microfinance institutions ( MFIs) is challenging as MFIs must achieve the twin objectives of outreach and sustainability. We propose a new measure to capture the performance of microfinance institutions by placing their twin achievements in a 2 × 2 grid of a classification matrix. To make a dichotomous classification, MFIs that meet both their twin objectives are

classified as ‘1’ and MFIs who could not meet their dual objectives simultaneously are designated as ‘0’. Six classifiers are applied to analyze the operating and financial characteristics of MFIs that can offer a predictive modeling solution in achieving their objectives and the results of the classifiers are comprehended using technique for order preference by similarity to ideal solution (TOPSIS) to identify an appropriate classifier based on ranking of measures of performance. Out of six classifiers applied in the study, KSVM (kernel lab-Support Vector Machines) achieved highest accuracy and lowest classification error rate that discriminates the best achievement of the MFIs’ twin objective. MFIs can use both these steps to identify whether they are on the right path to attaining their multiple objectives from their operating characteristics. Keywords: microfinance institution, growth and outreach, performance measure, classification algorithm, TOPSIS

1. Introduction The prime role of microfinance institutions (MFIs) is to expand economic opportunity to the poor (Shaw, 2008; Johnston & Morduch, 2008; Collins et al., 2009), which in turn can help in 1

reducing poverty and provide other socioeconomic benefits. Though this approach of providing financial services to the population excluded from formal financial sectors is laudable, these institutions should also be financially sustainable. Therefore, measuring performance of these institutions is influenced by the twin criteria of growth and outreach (Robinson, 2001, Hermes, et al., 2011). Debates on the role of MFIs are centered on two contrasting views: institutionalist and welfarist (Brau and Woller, 2004). According to the institutional, view it is necessary for MFIs to prioritize financial sustainability in order to make their operation successful. In contrast, the welfarist view is inclined towards social performance based on the common mission of MFIs to reduce poverty; and therefore, relying on grant and donations is justified. Trade-offs between the goals is difficult to bridge as cost of giving small loans to a large customer base is very high. Small loans increase both fixed and variable costs, as managing micro loans is information intensive and requires high monitoring cost (Conning, 1999). Fixed costs can be lowered by economics of scale that is by increasing outreach and variable costs can be managed by charging higher interest rates (Mersland and Strom, 2011). However, charging higher interest to poor borrowers is again undesirable. Therefore, the twin objectives of MFIs are somewhat contrasting and MFIs need to adopt a balanced approach. Whether the performance of MFIs is to be based on their profitability or on the outreach has not been adequately resolved (Morduch, 2000; Bos & Millone, 2015). Although there are various models of MFIs, and both for-profit and non-profit firms can coexist, validity of their twin goals has remained unchanged. Non-profit firms can exist endogenously in neo-classical settings (Lakdawalla and Philipsom, 2006) with donor grants and societal support and thus they can partly overcome market failure (Hirth, 1999), but considering such firms as a ‘going concern’ is questionable. According to Robinson (2001), MFIs that rely on subsidies and donation would be limited in outreach.

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There is no consensus in the literature regarding assessment of performance of MFIs. The performance of these MFIs has been traditionally evaluated through comparison of a number of ratios. In the present study, we propose a novel approach to measure performance of MFIs based on simultaneously achieving their dual objectives and compare their results with various physical and financial measures. Although MFIs provide an array of financial services to the poor, micro lending is the most important activity and a fair measure of outreach could be the increase in number of borrowers on a ‘year-to-year’ basis. Thus, an MFI that has been able to extend loan-related services to more number of borrowers, compared to the number of borrowers in the previous year, was considered successful in its outreach objective of the current year. Return on Asset (roa) is the most common measure of sustainability that can be used as an indicator of efficient use of capital. Maximizing roa has always been a key objective of forprofit organization, but, achieving a positive roa is a necessity even for the non-profits. MFIs failing to earn a positive roa are posing a threat to their own existence as a ‘going concern’, purely on financial concern. We therefore, classify MFIs into four quadrants based on their performance in the above two aspects as shown in Figure 1.

Figure 1. Proposed four quadrants based on the performance of MFIs As seen from Figure 1, MFIs in first quadrant (A) are meeting their twin objectives and are considered to be successful, whereas, MFIs in other quadrants are not able to perform well on 3

both fronts. MFIs in quadrant (B) are financially profitable but they could not fulfill their outreach objective and hence need to correct their operations. In contrast, the MFIs in quadrant (D) are able to increase the outreach goal but their financial viability is doubtful, such MFIs have to continually depend on donor support and outside funding. The MFIs in quadrant (C) are among the worst performers as none of their twin objectives is fulfilled. All MFIs regardless of their financial structure should strive to be placed in quadrant (A) where they will not only increase their client base on a year-to-year basis but also remain financially sustainable. To make a dichotomous classification, MFIs in quadrant (A) are therefore classified as successful and given binary code ‘1’ and other MFIs who could not meet their dual objectives simultaneously are placed in another binary class coded as ‘0’. Overall performance of the MFIs would depend on various operating and financial characteristics and hence we are applying several classifiers that can establish relationship between twin objectives of MFIs and their characteristics. As a number of classifiers are available, the goal is to assess the performance of the MFIs’ dual objectives through evaluating the classifier’s ability to predict correct binary classes i.e., meeting the dual objective or not. Eom and Lee (1987) formulated a global financing strategy using a large-scale goal programming model-based multi-objective decision support system. In the last few decades, numerous classification algorithms have been used in diverse research areas (Wong & Selvi, 1998; Cao & Parry, 2009; Bhattacharyya, 2011; Austin et al., 2013; Zhu et al., 2015). Hence, performance measurement is essential for model selection, i.e. to identify the most suited classification technique (Ali & Smith, 2006). Hand (2005 and 2006) has reported that some traditional performance measures such as the Gini coefficient, the Kolmogorov–Smirnov statistic, and the area under curve (AUC) measure are unsuitable for some problems that may lead to incorrect conclusions of a credit scoring problem. It is

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also worth mentioning that different classification algorithms differ on the accuracy of the predictions. Therefore, in the present study, we endeavor to analyze and comprehend the output of individual classifiers using a multi-criteria decision-making tool and try to identify the most suitable classifier for analyzing the performance of MFIs. Multi-criteria decision modeling (MCDM) is gaining popularity in managerial decision making for a wide number of business problems (Chandrasekaran & Ramesh, 1987; Triantaphyllou & Sánchez, 1997; Ngai, 2003; Choi et al., 2005; Chen, 2007; Doumpos & Zopounidis, 2011; Chen et al., 2013). The novel aspect of the proposed study is that MFIs are receiving funds from donors; their ability to raise funds would be affected if they fail to achieve both their objectives. In Figure 1, the MFIs in Quadrant C are not meeting any of the criteria and their survival is going to be at stake. They are showing positive roa but decreasing their outreach should increase their customer base even at a cost of reduction in roa. MFIs with negative roa must find ways to improve their operating performance as their sustainability is at stake. Objectives of the present study are as follows: 

The proposed study suggests an innovative grid-based framework to measure performance of MFIs based on their twin objectives.



Identification of best efficient classifier through estimating the various parameters of performance of each classifier after applying the training dataset would help to judge the ability of a MFI to meet the twin objectives when current performance data is applied into the model.



A number of classifiers are applied to analyze the operating and financial characteristics of MFIs that can offer a predictive modeling solution in achieving their objectives.

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

Results of the classifiers used in the study are comprehended using technique for order preference by similarity to ideal solution (TOPSIS) and suitable classifiers would thus be identified.



Overall, the paper endeavors to undertake a comprehensive methodology to appraise performance of MFIs.

The rest of the paper is organized as follows. Section 2 describes data; methods used in the study are explained in section 3. MCDM methods and their related experimental designs are discussed in sections 4 and 5. Results are analyzed and discussed in section 6. Finally, the paper is concluded in section 7. 2. Data description The required data for the analysis is sourced from Microfinance Information Exchange database (http://www.mixmarket.org), that has been used in a number of studies (Cull et al., 2009; Ahlin et al., 2011; Hermes et al., 2011; Bogan, 2012; Servin et al., 2012; Vanroose & D'Espallier, 2013; Tchuigoua, 2014) to analyze performance of MFIs. 2.1 Data Set and Data Preparation The database provides data of individual MFIs in a web-based format to present operational details of MFIs on a public platform and simultaneously ensure transparency. The database includes performance figures of more than 2500 MFIs. As annual financial results of a large number of MFIs for 2014 were not available in the database, we performed our analysis using operating and financial data for 2013. The analysis is focused on measuring performance of the MFIs on its dual objectives i.e., growth and outreach, and hence, we chose variables that can influence outcomes of these two criteria. However, a large number of economic parameters have been reported in literature to have implicated the performance of the MFIs for achieving both these dual objectives. A summary from literature on the variables selected

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in the present study from these wide number of influencing parameters on the MFIs performance are presented here. The breadth of outreach is exemplified by number of active loan per client. Whereas depth of outreach is measured by credit outstanding per client (Copestake, 2007). Lesser depth of outreach is indicated from the higher values of Average Loan Balance per Borrower as the less loans are provided to the poor borrowers by the MFIs (Hermes et al., 2011). The number of active borrowers defined the outreach (Vanroose and D’Espallier, 2013). The cost per borrower is a measure of efficiency and hypothesized to have negative impact on both the dual objective of MFIs (Arun and Murinde, 2010; Gonzalez, 2007). Debt/equity levels vary significantly amongst MFIs. Therefore, ROA is more suitable than ROE when computing financial outcomes across diverse MFIs (Mersland & Strøm, 2009). The ratio variables or economic parameters like Gross Loan Portfolio, Operating Expense/ Number of Active Borrowers (Gutierrez-Nieto et al., 2007), Personnel, Operating Expense / Assets, Financial Expense/ Assets and equity (Cull and Morduch, 2007), Portfolio at Risk > 30 days (Mersland and Strøm, 2009), Number of Active Borrowers (Hartarska and Nadolnyak, 2007), Borrowers per Staff Member (Kinde, 2012) have widely adopted for measuring the performance of MFIs. The list of independent variables used in the study to analyze performance of MFIs is provided in Table 1. Table 1. Selected variables of the dataset used in the experiment Symbol Variable asst Assets alpb Average Loan Balance per Borrower borr Borrowings bpsm Borrowers per Staff Member cpb Cost per

Description Total of all net asset accounts Loan Portfolio, Gross / Number of Active Borrowers

Borrowings of MFI Number of Active Borrowers / Personnel Operating Expense/ Number of Active Borrowers , average 7

eqt ab13

fea

glp

oea

pers pr30

Borrower Equity Number of Active Borrowers

Financial Expense / Assets (%) Gross Loan Portfolio

Operating Expense / Assets (%) Personnel Portfolio at Risk > 30 days

Total of all equity accounts, less any distributions. The number of individuals or entities who currently have an outstanding loan balance with the MFI or are primarily responsible for repaying any portion of the Loan Portfolio, Gross. Individuals who have multiple loans with an MFI should be counted as a single borrower. Financial Expense/ Assets, average

All outstanding principal for all outstanding client loans, including current, delinquent and restructured loans, but not loans that have been written off. It does not include interest receivable. It does not include employee loans. Operating Expense/ Assets, average

Total number of staff members. The value of all loans outstanding that have one or more installments of principal past due more than 30 days. This includes the entire unpaid principal balance, including both the past due and future installments, but not accrued interest. It also includes loans that have been restructured or rescheduled.

Sources: http://www.mixmarket.org/about/faqs/glossary and http://www.gdrc.org/icm/glossary/ Variables such as asst, alpb, borr, est, ab13 and glp are measures of outreach, whereas variables such as bpsm, cpb, fea, oea, pers and pr30 are measures of efficiency. Since there are several missing data in the Microfinance Information Exchange database, we excluded MFIs that have missing information on any of the variables used in the study. After taking care of the missing data, finally 5841 MFIs across the globe formed our dataset to be used in the experiment for the proposed research. To classify the performance of MFIs into two binary classes, following actions have been undertaken for determining the dependent or target variable (used in the study as pred). MFIs that increased number of active borrowers from 2012 to 2013 were considered as having met their outreach objective and MFIs that reported positive return on assets were considered financially sustainable. Only those MFIs that met both the twin criteria were considered as

1

Selected only 584 MFIs without missing information. This aspect might have some selection bias.

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class “1” and others who could not meet either or both of these criteria were classified as “0” category. Descriptive statistics for the 12 predictor variables used in the study are presented in Table 2. Table 2. Descriptive statistics of the original dataset variables

Mean

Median

Standard Deviation

Minimum

Maximum

ab13

1.34E+05

1.49E+04

5.74E+05

9.00

7.10E+06

asst

1.21E+08

1.48E+07

4.34E+08

9042.00

6.13E+09

glp

9.51E+07

1.16E+07

3.53E+08

4722.00

5.77E+09

eqt

2.02E+07

4.10E+06

6.45E+07

-4.77E+07

8.37E+08

borr

3.00E+07

3.99E+06

9.79E+07

0.00

1.51E+09

alpb

1704.06

752.50

3069.04

17.00

4.49E+04

fea

0.05

0.05

0.04

0.00

0.33

oea

0.19

0.14

0.16

0.00

1.63

cpb

264.67

180.50

434.93

0.00

6708.00

bpsm

135.83

103.00

114.02

3.00

831.00

pr30

0.28

0.03

5.47

0.00

132.28

pers

661.49

150.50

1803.48

2.00

2.19E+04

3. Data mining methods In this study, we applied six binary classification data mining models, as implemented in the rminer package of the R-tool (Cortez, 2010): MLP (Multilayer Perceptron), KSVM (kernel lab-Support Vector Machines), LDA (Linear Discriminant Analysis), QDA (Quadratic Discriminant Analysis), k-NN (k-Nearest Neighbors) and neural network. Data mining tools for the present study have been chosen as representation from both statistics and artificial intelligence. Data mining jobs can be classified into two categories (Fawcett, 2006): descriptive, where the intention is to characterize the properties of the data; and predictive, to forecast the unknown value of an output target given known values of other variables (the inputs). Predictive tasks can be further divided into classification, when the output domain is discrete, and regression, when the dependent variable is continuous. The task of classification using data mining involves two stages: development of classification model and assessment of data mining classifier models. During the first stage, 9

the selected classifier is trained by a trained dataset to develop a predictive classification model. A testing dataset is applied in the next stage to assess the classifier’s ability for the selected model. All the classifiers were assessed using 10 runs of a 10-fold cross-validation method during development and testing phase. The mining function executes numerous fits and returns a list with the achieved predictions. A number of classification algorithms: LR, MLP, LDA and QDA have been applied in literature to assess the efficiency of the MFIs by developing credit scoring model and evaluating the models’ performance using area under the receiver-operating characteristic curve (AUC) and misclassification costs (Blanco et al., 2013; Kiruthika and Dilsha, 2015; Cubiles-De-La-Vega et al., 2013 ). In a related work, support vector machine model was successfully applied in correct prediction of credit scoring problem (Zhong et al., 2014). A logistic regression (LR) can be used to predict the achievement of MFIs’ dual objectives of growth or outreach. The LR model as a non-linear regression model is a specialized form of generalized linear model (Schumacher et al., 1996; Menard, 2009). The objective is to identify the optimal model that defines association between the dependent or response variable and the 12 explanatory variables. The response variable takes the binary values of ‘1’ when the dual objectives are met; otherwise, it takes ‘0’ when objectives are not met. Thus, the binary classification using the LR model can be defined as (1): 𝑝

𝑝

𝑔(𝑥 ) = log (1−𝑝) = 𝛽0 + 𝛽1 𝛽𝑥1 + 𝛽2 𝛽𝑥2 + ⋯ + 𝛽𝑖 𝛽𝑥𝑖 = 𝛽0 + ∑𝑖=1 𝛽𝑖 𝑥𝑖 , … (1) where p is the probability of the outcome of interest (response variable), the intercept β0 is a constant parameter, the coefficients β1,…,βi are related for each independent variable x1,…,xi. Iteratively, βi is computed from log-likelihood function. This is a general binary classification model that applies a smooth nonlinear logistic transformation over a multiple regression algorithm by estimation of the class probabilities (Venables & Ripley, 2002). The advantage

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of the model is due to the least assumption on the normal distribution and easy explanation of the outcome. Neural networks are a kind of connectionist models motivated by the behavior of the human brain (Haykin, 2009). One of the most popular neural network architectures is multilayer perceptron (MLP) where processing nodes are collected into layers and coupled by weighted links. The MLP is activated by providing the input layer with the input variables and then propagating the activations in a feedforward fashion, via the weighted connections, through the entire network. In the present study, a completely inter-connected network having only one hidden layer of H nodes with one output node has been adopted. The complexity of the learning ability of the model would be taken care by the H hyperparameter. We have applied the MLP model from nnet package that used one hidden layer of H neurons with logistic functions as given in equation 2: 𝐼+𝐻

𝐼

𝑦𝑖 = 𝑓𝑖 (𝑤𝑖,0 + ∑ 𝑓𝑗 (∑ 𝑗=𝐼+1

𝑥𝑛 𝑤𝑚,𝑛 + 𝑤𝑚,0 ) 𝑤𝑖,𝑛 )

(2)

𝑛=1

For node i, the output is 𝑦𝑖 with 𝑤𝑖,𝑗 as weight from j to I node, and fj is the activation function for node j. Only one output neuron with logistic function is applied for classifying binary class. Discriminant analysis is similar to the model that groups the objects x into the class y  0,1 with the largest discriminant score that is computed on basis of equal priors (Johnson & Wichern, 1988). The goal is to obtain the posterior probability for optimal classification (Bishop, 1996; Ledolter, 2013). The basic assumption of LDA is that both populations are multivariate normal with means 1 ,  2 and a mutual covariance  given two independent samples with p quantitative target variables for ni observations (i= 1, 2) and n=n1 +n2. The LDA classifier separates a pdimensional vector x to class 2 when the equation 3 satisfies. 11

−1

̂ ( 𝑥 ′ ̂2 −  ̂1 ) >

1 ′ −1 1 ′ −1 ̂  ̂  ̂2   ̂2 −  ̂  ̂1 + log̂ 1 − log̂ 2 2 2 1

(3)

The π1 and π2 are a priori class membership probabilities, computed by the ratios of the classes in the training set. LDA is testified as a more robust and accurate model (Dillon et al., 1984). We have applied LDA function from MASS library of R package (Venables and Ripley, 2002). The LDA function generates the predictable probability for each class and thus the rule of classification is based on the greater or less value of threshold probability pc that could be finalized after optimizing the error of classification. In LDA, the linear functions of the variables are applied to define or explain the relationships between two or more groups (Yu, 2008). However, when the covariance  is supposed to be different, then the quadratic discrimination functions are calculated and thus the QDA rule is (equation 4): 1

′ −1

1

̂i | − (𝑥 −  ̂ (𝑥 −  arg max 𝑖 (𝑥 ), 𝑖 (𝑥 ) = − 2 log| ̂1 )  ̂𝑖 ) + log ̂i 2

(4)

Both the LDA and QDA classifiers are found to apply successfully (Pino-Mejías et al., 2010; Mostafa et al., 2013) using the MASS library of R package (Venables and Ripley, 2002). Surprisingly, the main demerit of LDA has been reported for its simplicity as it is unable to capture the complexity of the dataset (Pino-Mejías et al., 2010). Conversely, the QDA necessitates a huge number of factors, and inclines towards overfitting on datasets. Thus, LDA is commonly superior, due to its robustness without having any assumptions. Both the LDA and QDA are reminiscent of logistic regression/probit models. Vapnik et al. (1995) have proposed the SVMs as a novel classifier and regression. As a classifier, SVMs identify the optimal separation between two classes in the independent vector space (everything to one side is 0, everything on the other side is 1) with probabilistic distribution of learning vectors in the dataset. The objective of SVMs is to explore the best possible hyperplane boundary that distinguishes both binary classes when both classes are linearly separable and thus SVMs correctly separate the two classes even for unknown 12

samples. In case of non-linearly separable classes, a kernel function such as Gaussian radial basis function is applied that transforms the input x∈ℜI into a higher m-dimension (Berrueta et al., 2007) to identify the best linear separable hyperplane with respect to a set of support vectors in the feature space. SVMs show more theoretical advantages than neural networks through their better generalization ability and absence of local minima during their training phase (Hastie et al., 2008). The ability of classification in SVMs is influenced by two hyperparameters: ϒ, the kernel parameter, and C, a parameter for penalty. The probabilistic SVM output is given by (Wu et al., 2004) equations 5 and 6: 𝑚

𝑦𝑗 𝑗 𝐾(𝑥𝑗 , 𝑥𝑖 ) + 𝑏

(5)

𝑝(𝑖 ) = 1/(1 + exp(𝐴𝑓(𝑥𝑖 ) + 𝐵),

(6)

𝑓 (𝑥 𝑖 ) = ∑

𝑗=1

where m is the number of support vectors, yi ∈ {-1, 1} is the output for a binary classification, b and αj are coefficients of the model, and A and B are determined by solving a regularized maximum likelihood problem. In rminer, the transformation (φ(x)) is determined by a kernel function either by using the sequential minimal optimization (SMO) or a Gaussian kernel (with fewer parameters than other kernels such as polynomials) as shown in equation 7: 𝐾(𝑥, 𝑥 ′ ) = exp(−𝛾 ‖𝑥 − 𝑥′‖2 ), 𝛾 > 0.

(7)

The SVM algorithm identifies the optimal linearly separable hyperplane given by equation 8. 𝑦𝑗 = 𝑤0 + ∑𝑚 𝑖=1 𝑤𝑖 ∅𝑖 (𝑥)

(8)

As the search space for the above parameters is high, a default heuristic is chosen, where C = 3 for a standardized output. In the diverse domain of management research, SVMs are successfully applied in financial area (Ravi et al., 2008; Carrizosa et al., 2010), churn analysis (Coussement & Van den Poel, 2008), etc. To the best of our knowledge, no application has 13

been explored on the use of SVMs in the microfinance performance classification. In the present study, a robust application of SVM function for the implementation of SVM algorithm has been applied as found in R software (Dimitradou et al., 2005) In k-NN model, the prediction is done on basis of the outcome of the k most similar observations in the dataset. The objective of k-NN is to identify k-objects in the training dataset that are equal to a new object which needs to be classified (Shmueli et al., 2007). The label of the class is then ascribed on basis of the class of most of the k-nearest neighbours. By selecting the k odds, conflict can be avoided. As a practice, the Euclidean distance is used for computing the similarity measure. A grid search is applied to optimize the hyper-parameters of both MLP and SVM (e.g., H, 𝛾). To avoid overfitting, an internal k-fold is applied to all the six chosen data mining models. 3.1 Performance score A variety of measures for classifiers exists in the literature for diverse purposes of evaluating. In literature, a number of study have been shown to achieve better performance for given classifiers on a dataset. This may not be a good classifier when applying different measures (Ali & Smith, 2006; Ferri et al., 2009). Moreover, the performance of the classifiers may be influenced by the features of datasets such as size, distribution of class, or noise. Therefore, the assessment of the classifiers using only one or two measures of performance is often found not suitable. The present study endeavors to develop a comprehensive assessment of quality of binary classifiers assuming the above two considerations through employing a set of measures on the dataset related to the performance measures of MFIs. The simple notion of this comprehensive metric is comparable with the ranking methods that will apply the outputs from classifiers on MFI datasets to rank those classifiers (Brazdil & Soares, 2000; Peng et al., 2009).

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3.2 Selection of performance measures The performance of a classifier’s ability to generate a good solution is being assessed using a confusion matrix (Kohavi et al., 1998) in a tabular form. Table 4 presents the predicted and actual/target class classification generated by the classifier applied on a binary classification problem. Evaluation of classifiers is a critical decision for the present study. Even the predictive accuracy being a most widely used measure for classifier’s performance often becomes misleading with unbalanced data. For example, in the present problem, 40% and 60% of the MFIs are poor and good performers, respectively, to achieve the dual goal. For evaluating the performance of classifiers, specificity and sensitivity are two vital measures amongst all the measures mentioned in Table 3. Sensitivity identifies the percentage of true positive rate while specificity defines the percentage of true negative rate. The positive predictive value (precision) is the proportion of the predictive positives which are actually positive. The negative predictive value calculates the percentage of positive and negative characteristics in case of positive and negative tests, respectively. Ideally for computation of performance, specificity and sensitivity should have equally high value. The classification error is defined as: (fp + fn) / (total samples), whereas the balance error rate (BER) is defined as half of the total error rate. The predictive accuracy (ACC) of classification is the most widely used measure of performance for the classifiers. The ACC sometimes is misleading for unbalanced data with an inadequate classification objective. Therefore, a potential solution may be to use several measures of performance as a solution to this problem. Thus, in this study, we have also employed kappa and AUC as performance measures. The ROC (Cheng et al., 2006) is a 2-D plot of TPR (sensitivity) versus fpr (1-specificity) in vertical and horizontal axes, respectively. The AUC is another crucial and reliable measure where the value of 1.0 is an ideal performance for the assessment of the classifier.

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On the other hand, KAPPA (also calculated from the confusion matrix) is a substitute measure to accuracy rate, as it compensates for random hits (Cohen, 1960; Smith, 1983). Comparing with the common classification rates, kappa calculates the portion of hits that can be attributed to the classifier itself (i.e., not coincidental), relative to the total classifications that cannot be attributed to chance alone (Galar et al., 2011). It is less sensitive than the ROC curves as being a scalar measure. Based on the scoring of the correct classifications, both the classification rates and kappa can be compared. Classification rate scores all the successes over all classes, whereas kappa scores individually for the successes of each class and aggregates them. Thus, it becomes less sensitive to randomness caused by a different number of examples in each class. The study has also considered computational time for each model. Table 3. Confusion Matrix for binary classification with the common measures

Performance measures

 Actual data class

Confusion Matrix

Classified as 

+ve

+ve

True Positive False (tp) Negative (fn)

-ve

False Positive True (fp) Negative (tn) Positive predicted value (precision) =tp/(tp+fp)

Performance measures

Decisions/ Actions from the model

True positive rate (sensitivity)=tp/ (tp+fn) True negative rate (specificity)= tn/(tn+fp)

Meet dual objective

-ve

Negative predicted value=tn/(tn+ fn)

Accuracy= (tp+fn)/total number observations

Not-meet dual objective

of

4. MCDM method: Technique for order preference by similarity to ideal solution (TOPSIS) For assessing the performance of the classifier algorithms, usually more than one measure needs to be examined such as accuracy, AUC, kappa, classification errors, etc. Thus, the

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selection of classifiers can be demonstrated as MCDM problems. There are various MCDM approaches that can be applied to rank alternatives. In the present study, TOPSIS has been chosen because of its credible performance as reported in previous research and ease of application (Agrawal et al. 1991; Zanakis et al. 1998). Hwang and Yoon (1981) originally proposed the TOPSIS method to rank alternatives over multiple criteria. Since then, TOPSIS has been reported to be applied in various forms (Kim et al., 1997; Wang et al., 2014; Kou et al., 2014). It discovers the best choices by reducing the distance to the idea solution and maximizing the distance to the nadir or negative-ideal solution (Olson 2004). The following approach of TOPSIS has been adopted from Opricovic & Tzeng (2004) and Olson (2004) for use in the experiment to rank the classifiers: Step 1: Calculate the normalized decision matrix. The normalized value rij is calculated as: 𝐽

𝑟𝑖𝑗 = 𝑥𝑖𝑗 /√∑

𝑗=1

2 𝑥𝑖𝑗 ,

𝑗 = 1, … , 𝐽;

𝑖 = 1, … , 𝑛,

(9)

where J and n denote the number of alternatives (i.e., classification algorithms) and the number of criteria (i.e., performance measures), respectively. For alternative Aj, the performance measure of the ith criterion, Ci is represented by xij. Step 2: Develop a set of weights wi for each criterion and calculate the weighted normalized decision matrix. The weighted normalized value vij is calculated as: 𝑣𝑖𝑗 = 𝑤𝑖 𝑥 𝑖𝑗 , 𝑗 = 1, . . . , 𝐽; 𝑖 = 1, . . . , 𝑛,

(10)

where wi is the weight of the ith criterion, and ∑𝑛𝑖=1 𝑤𝑖 = 1. Step 3: Find the ideal alternative solution S+, which is calculated as: 𝑆 + = {𝑣1+ , … , 𝑣𝑛+ } = {(max𝑣𝑖𝑗 |𝑖 ∈ 𝐼 ′ ) , (min𝑣𝑖𝑗 |𝑖 ∈ 𝐼 ″ )} , 𝑗

𝑗

(11)

where I′ is associated with benefit criteria and I′′ is associated with cost criteria. For the evaluation of default prediction models, ACCURACY, KAPPA, TPR, PRECISION0,

17

PRECISION1 and AUC are benefit criteria and have to be maximized and CE, BER, TNR are cost criteria and have to be minimized. Step 4: Find the negative-ideal alternative solution S−, which is calculated as 𝑆 − = {𝑣1− , . . . , 𝑣𝑛− } = {(min𝑣𝑖𝑗 |𝑖 ∈ 𝐼 ′ ) , (max𝑣𝑖𝑗 |𝑖 ∈ 𝐼 ″ )} 𝑗

(12)

𝑗

Step 5: Calculate the separation measures using the n-dimensional Euclidean distance. The separation of each alternative from the ideal solution is calculated as 𝑛

𝐷𝑗+

= √∑(𝑣𝑖𝑗 − 𝑣𝑖+ )2 , 𝑗 = 1, . . . , 𝐽

(13)

𝑖=1

The separation of each alternative from the negative-ideal solution is calculated as 𝑛

𝐷𝑗− = √∑(𝑣𝑖𝑗 − 𝑣𝑖− )2 , 𝑗 = 1, . . . , 𝐽

(14)

𝑖=1

Step 6: Calculate a ratio R+j that measures the relative closeness to the ideal solution and is calculated as 𝑅𝑗+ = 𝐷𝑗− /(𝐷𝑗+ + 𝐷𝑗− ), 𝑗 = 1, … , 𝐽.

(15)

Step 7: Rank alternatives by maximizing the ratio 𝑅𝑗+ 5. Experimental design The experiment has been performed on an Intel Core i7 3.40GHz machine in Windows environment using rminer tool of R-package (www.r-project.org). The experiment was carried out according to the following process: Input: A performance dataset of MFIs described in section 2.1. Output: Comprehensive performance ranking of six classification algorithms considering 9 measures. The experiment was performed on basis of the following stages: BEGIN

18

Step 1: Develop actual datasets: choosing and transforming the relevant variables; cleansing of data Step 2: Train and test the six selected classifiers on a randomly sampled partitions (i.e. 10-fold cross-validation) using rminer package of R-software (Cortez, 2010) and as per Section 3 Step 3: Selection of 9 performance measures (except computation time) to assess the performance of binary classification algorithms as discussed in Section 3.2. Step 4: Develop a comprehensive performance measure to evaluate six classifiers using TOPSIS based on MCDM approach as illustrated in Section 4 taking equal weight for each measure in TOPSIS. Step 5: Obtain the overall ranking of the 5 classifiers for their best classification ability using the TOPSIS tool. Step 6: Identify the best predictive model capable to discover the dual performance objectives of the MFIs. Go to Step 2 else End Step 7: Recalculate the rankings of classifiers using the TOPSIS methods with the ranking produced in Step 4. END 6. Results and Discussion Table 4 shows the classification results of MFIs performance data. Each column denotes the number of data counts in a predicted binary class and each row characterizes the number of data counts in a target or actual binary class. For individual classifiers, values on the diagonal of the confusion matrix are correct classification and the remaining values are incorrect classification of the MFIs’ performance data. The finest accuracy for each predicted class is highlighted in boldface and italic. However, it is evident from Table 4 that there is no single classification algorithm which succeeds the best outcomes for both the binary classes. The results of different performance metrics using the six different classifiers of the experiment undertaken are presented in Table 5. As shown in Table 5, KSVM achieved highest accuracy (ACC) (66.92%) and lowest classification error rate is 33.08% amongst all classifiers. Ideally, it is desirable for a good classifier to achieve higher and lower values for the metrics accuracy and error, respectively. However, AUC is higher for LDA and PRECISION2 is higher for QDA. Thus, different performance measures provide different evaluation of different classifier performance. More interestingly, k-NN achieved consistent measures of performance with respect to all the

19

metrics applied in the experiment. Therefore, the TOPSIS as one of the MCDM methods would be applied in the next step to generate a final ranking of the six classifiers to build up a comprehensive performance measure. Table 4. Classification results of MFIs performance

KSVM

LDA

k-NN

QDA

MLP

target 0 1

predicted as 0 1 88 144 50 302

target 0 1

predicted as 0 1 90 142 53 299

target 0 1

predicted as 0 1 108 124 91 261

target 0 1

predicted as 0 1 203 29 83 269

target 0 1

predicted as 0 1 111 121 106 246 predicted as 0 1 137 95

target

LR

0 1

60

292

Table 5. Output of selected performance measures of six classifiers undertaken in the experiment

MLP

ACC

CE

BER

KAPPA

TPR

TNR

PRECISION0

PRECISION1

AUC

60.84

39.16

40.85

18.30

67.36

50.95

50.86

67.62

0.61

20

Computational time (second) 5.41

KSVM

66.92

33.08

37.98

25.81

85.85

38.19

64.05

67.82

0.67

1.40

LDA

66.59

33.41

38.17

25.32

85.00

38.66

62.92

67.78

0.69

0.46

QDA

49.02

50.98

44.40

9.54

23.61

87.59

43.07

74.40

0.63

0.45

k-NN

63.18

36.82

39.65

21.22

74.15

46.55

54.33

67.79

0.64

0.25

LR

66.34

33.66

37.99

25.44

83.07

40.95

61.44

68.12

0.68

2.41

In the next step, to develop a comprehensive measure of assessment for the six different classifiers using the above 10 performance measures, ranks are assigned as provided in Table 6. In this table, except for classification error, balanced classification error (BER) and true negative rate (TNR), in rest of the 6 measures, rank is assigned in such a way that lower the rank value means better the performance of the classifiers. The measures PRECISION0 and PRECISION1 represent precision measures for binary class ‘0’ and ‘1’, respectively. Table 6. Rank wise arrangement of performance measures obtained from six classifiers ACC

CE

BER

KAPPA

TPR

TNR

PRECISION0

PRECISION1

AUC

MLP KSVM LDA

5 1 2

5 1 2

5 1 3

5 1 3

5 1 2

5 1 2

5 1 2

6 3 5

6 3 1

QDA k-NN

6 4

6 4

6 4

6 4

6 4

6 4

6 4

1 4

5 4

LR

3

3

2

2

3

3

3

2

2

In order to combine output of different performance measures, we employed TOPSIS approach as a solution to MCDM as this approach can combine both ascending and descending directional vectors to a common score. A comprehensive ranking for different classifiers using TOPSIS is provided in Table 7. As per Table 7, KSVM is the best classifier followed by LDA, LR, k-NN, MLP and QDA. Table 7. Overall rank calculated using TOPSIS from the rank performance measures of six classifiers Classifiers KSVM

score rank 1 0.942 21

LDA LR k-NN MLP QDA

0.940 0.926 0.763 0.641 0.060

2 3 4 5 6

The results presented in Tables 4, 5, 6 and 7 show that the rankings computed by the TOPSIS approach for six classifiers from 9 measures are now in robust agreement. When the common measures are considered with the objective to predict the best performer MFIs, then KSVM, LDA and LR are the best classifiers. Figure 2a and b show the ROC curve for the six classifiers. These are generated by plotting the TPR and FPR for a range of different cut-off values. The point on the curve that is closest to the upper left corner represents the cut-off value that will maximize the sensitivity and specificity of the classification (Hosmer et al., 2013). In this study, determination of the classifier’s ability is being performed through discriminating the achievement of the MFIs’ twin objective. Figure 2a and 2b clearly favours the KSVM and LDA as best classifiers. However, Kohavi et al., (1998) reported that ROC analysis is not as simple as comparing with a single number. An area of 0.5 indicates no discrimination between the two outcomes and an area greater than 0.65 is considered as good discrimination. The AUCs for LDA, LR and KSVM are 0.69, 0.68 and 0.67, respectively. There are no specific settings for parameters and rules that lead to a good model for any of the six applied models (Kiruthika & Dilsha, 2015). Every model has its own advantages and disadvantages as listed in Table 8 for predicting the MFIs performance. The superiority of performance of a specific model depends on the specific dataset applied in the model. Therefore, TOPSIS as a MCDM tool correctly captured the true reflection of the overall performance of the classifiers with respect to all the 9 measures in a single ranking. Based on the novel objective set designed on a grid-based framework for measuring performance of MFIs, we have defined twin objectives consist of outreach objective: MFIs

22

that increased number of active borrowers from 2012 to 2013 and financially sustainable objective: MFIs that reported positive return on assets. Thus, in our binary dependent variable only those MFIs that met both the twin criteria/objectives were considered as class “1” and others who could not meet either or both of these criteria were classified as class “0”. Our study reveals the applied six classifier’s ability to predict the “0” and “1” and evaluated their performance using various measures of performance of each classifier after applying the training dataset that would help to judge the ability of a MFI to meet the twin objectives when current performance data is applied into the mode. Out of six classifiers, KSVM achieved highest accuracy (ACC) (66.92%) and lowest classification error rate is 33.08% that discriminates the best achievement of the MFIs’ twin objective (i.e., class “1”). Hence, this classifier can be used to predict the achievement of MFI’s twin objectives based on its various operating and financial performance data.

Figure 2a. ROC for class 0 (‘0’ denotes: not meeting twin objectives)

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Figure 2b. ROC for class 1 (‘1’ denotes: meeting twin objectives) Table 8. Comparative advantages and disadvantages of the six applied models to classify the successful MFIs in achieving the twin goals Classification Advantages Disadvantages models LR  Theoretically, better performing on the  Difficult to make features that are roughly linear and where incremental. problem to be separated is linearly  Misclassification cost separable. (FP and FN) is more  Implementing it as non-linear regression model also improved the performance in classifying achievement of MFIs dual objectives KSVM  Generally, KSVM is more suited for binary  Identifying a better and classification problem that is non-linearly precise kernel becomes separable and related with high difficult dimensionality. Theoretically, the KSVM  May become less is more advantageous as there is no local efficient with a very minima during the training of the model. large number of training data  KSVM with a specific non-linear kernel like radial basis function achieves superior classification performance and also ensures overfitting issues.  In the present work KSVM becomes more favourable and efficient as it is applied to comparatively lesser number of training dataset k-NN  As being a complete non-parametric  Performed moderately model, so there is no need to assume on the in classifying the 24

LDA

QDA

MLP

shape of the decision boundary.  It successfully classifies the binary values: achieving the dual objectives or not  more restricting Gaussian assumptions than LR ensures better performance in binary classification  Possibly the performance is better due to moderately large explanatory variables are used (12 variables).  It is a compromise of k-NN and LDA and LR models and assumes on quadratic decision boundary. Thus, successful in classification with lesser learning examples.  The important advantages of MLP are: nonlinear learning and more flexibility.

achievement of dual objectives of MFIs  Suffers from normality conditions.

 It is less flexible than kNN and least performer in classifying the binary objectives  Identify the correct and optimal architecture and topology is hard  Learning takes longer time  One of the least performer in the present classification task

6.1 Knowledge-enriched performance measurement of MFIs Although classification techniques could be used as an important basis for analyzing financial and operating performance of any enterprise, most of the studies concentrate on improving the existing classification algorithm that can identify patterns without paying adequate attention to how these classifiers can be applied in real life situations. The lack of interaction between academic data mining researchers and line managers is the primary reason for inadequate applications of sophisticated data mining tools in the real world (Peng et al., 2011). We made an attempt to use several classification algorithms for measuring performance in the context of MFIs. These institutions differ from usual profit-oriented organizations and have to meet two contrasting objectives simultaneously. In absence of any routine analysis methods to combine these two objectives into a single classifier, we implemented a novel approach of classifying performance on a 2×2 dimensional grid, which 25

was further segregated into a binary set-up based on whether the MFIs have achieved their twin objectives. We applied six classifiers to the dataset with ten-fold cross-validation to make classification results more reliable. Classifiers with low false negative rate can be useful to the MFIs to know their bad results in advance so that they can take remedial actions before the final results are available. In our dataset, KSVM classifier has the lowest false negative rate and this classifier also emerged as the best performer when 9 different accuracy measures were combined using TOPSIS. It is found that appropriate selection of data mining techniques can enrich performance measurement system of MFIs.

7. Conclusion and Future Research The purpose of the present study was to prepare a framework to measure the performance of MFIs that simultaneously strive to achieve their twin objectives of achieving growth and outreach. Initially, we classified the performance of MFIs into four grids described in Figure 1 and endeavored to classify the MFIs that are most likely to belong to quadrant (A) based on their current operational and financial parameters using the six different classifiers. Performance of each binary classifier was measured using 9 different parameters in order to identify the best classifier. As different classification techniques are likely to give different accuracy of prediction, this paper developed a MCDM approach to resolve conflicting rankings generated by the classifiers and obtained a compromised solution to secure an optimal ranking using the TOPSIS method. When common measures are considered with the objective to predict the best performer MFIs, then KSVM, LDA and LR are found to be the best classifiers.

26

Predicting the performance of any organization can help them change the course of action in order to improve its performance. MFIs can use these steps to identify whether they are on the right path to attaining their multiple objectives from their operating characteristics. To summarize, this study demonstrates that the appropriate selection of classifier can be useful in measuring the performance of a MFI. Based on availability, data for the year 2013 were selected to apply in the present work. A similar experiment can be done with the latest data following the steps discussed in the study. With the changed dataset, the training and testing samples would differ and preferred classifiers may also be different. However, the framework suggested in the paper, to judge the performance of MFIs based on fulfilling its twin objectives would remain same and valid. The potential aspect to consider in future also lies with incorporating region and few other variables, panel data, applying ensemble model, etc. The availability of data without missing information is the major limitation as the present study considered only 584 MFIs out of more than 2500 MFIs. In future, the scope of the present problem can be modeled with multiple performance criteria instead of achievement of dual goals as a binary problem. Even each criterion can be represented by some scale factor in lieu of a dichotomous decision. Therefore, there is an opportunity in future research to apply a better predictive model to solve the multiple performance criteria problem with scaled decision. References [1] Agrawal VP, Kohli V, Gupta S (1991) Computer aided robot selection: the multiple attribute decision making approach, International Journal of Production Research 29(8): 1629–1644. http://dx.doi.org/10.1080/00207549108948036 [2] Ahlin C, Lin J, & Maio M (2011) Where does microfinance flourish? Microfinance institutions performance in macroeconomic context. Journal of Development Economics, 95:105–120.

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