4. Methodology
4.4. Model Specification
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立 政 治 大 學
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4. Methodology 4.1. Research Approach
In this paper, there are two types of research approaches we use in order to solve the research problem which include the qualitative and the quantitative approaches. We use the quantitative method to test research hypotheses and qualitative research to uncover trends in thought and opinions that related to the research problem.
4.2. Data Source and Type
One of the significant features of research is the decision making about to collect the research data, from and in what ways the data should be collected. In this study, we use both primary and secondary data.
For the primary data, the researcher uses a questionnaire as the main tool for collecting data for the analysis. The questionnaires of this research include both close and open-ended questions. We prepare the questionnaires in English first before translating to Lao and we also conduct a pre-tested by the pilot study before conducting the survey for the whole sample.
Additionally, we conduct qualitative data through semi-structured, face to face interviews with field staff/village bank consultant, manager and development advisor of the Saving and Credit Union Champa Phatthana in order to get an in-depth understanding of the problem. For the secondary data, the materials include microfinance history, and the number of microfinance institutions and its clients.
4.3. Target Population
The population for this research is borrowers of the village banks under the support of the Saving and Credit Union Champa Phatthana (SCU). The target group includes both defaulters and non-defaulters of the village banks’ clients.
4.4. Model Specification
Loan repayment is a dependent variable, while different borrower’s characteristics, borrower's financial conditions, culture, loan features, travelling time from SCU office to clients and borrower’s experience with moneylenders are the independent variables. In this research, the dependent variable assumes values 0 and 1, which is 1 is a defaulter and 0 if the borrower
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國立 政 治 大 學
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N a tio na
l C h engchi U ni ve rs it y
is a non-defaulter. Consequently, we treat loan repayment as a dichotomous dependent variable and a non-continuous dependent variable which does not fit the key assumption in the linear regression analysis.
Statistically, logistic regression or logit model is a regression model where the dependent variable(DV) is categorical that the output can take only two values, “0” and “1”. For example, the outcome can be pass/fail, win/loss, default/non-default. However, there are some cases where the dependent variable has more than two outcome categories, researcher may use multiple logistic regression, or if the multiple categories are in order, researcher may apply the ordinal logistic regression to analyze the data.
Even though there are several methods we can use to analyze the data involving binary outcomes but the logic model is the best fit for this study because the logit model best fits the non-linear relationship between the dependent and independent variables and it has only two outcomes. Moreover, a logistic model has its simplicity of calculation and its probability lies between 0 and 1. The probability comes near zero indicates an unlikely event or the value of the explanatory variable gets smaller and the probability near 1 indicates a likely event or the value of the explanatory gets larger, (Jote, 2018).
David Cox is the statistician who developed the logistic regression in 1958. The binary logistic model is used for the estimation of probability of a binary response based on one or more predictors (variables). It allows one to say that the present of a risk factor increases the odds of a given outcome by a specific proportion. Since the dependent variable of this research (loan repayment) has binary outcomes (defaulter and non-defaulter); hence, in this the binary logistic regression is the best fit for this study.
The analysis of determinants of the loan repayment problem uses a binomial logistic model, interest lies primarily in the response probability.
𝑃(𝑦 = 1|𝜒) = 𝑃(y = 1|𝑥1, 𝑥2… , 𝑥𝑘)| (1)
𝑃(𝑦 = 1|𝜒) is the probability that y=1(defaulting) given x (independent variable), y represents loan repayment and X denote the full set of explanatory variable that include
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國立 政 治 大 學
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N a tio na
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borrower’s characteristics, borrower's financial conditions, culture, loan features, travelling time between borrowers and MFI and loan from moneylenders.
𝑃(𝑦 = 1|𝜒) = 𝐺(𝛽0+ 𝛽1, 𝑥1… + 𝛽𝑘, 𝑥𝑘) = 𝐺(𝛽0+ 𝑥𝛽) (2) where G is a function taking on values strictly between zero and one: 0 <G(z)<1, for all real numbers z. This ensures that the estimated response probabilities are strictly between zero and one. We write 𝑥𝛽 = 𝛽1𝑥1+ ⋯ + 𝛽𝑘𝑥𝑘. Logistic function is a non-linear function used for the function G in order to make sure that the probabilities are between zero and one. In the logit model, G is the logistic function which is between zero and one for all real numbers z. This is the cumulative distribution function for a standard logistic random variable.
𝐺(𝑧) = exp(𝑧) /[1 + exp (𝑧)] (3) where Z = X𝛽= 𝛽1, 𝑥1… + 𝛽𝑘, 𝑥𝑘. The goal of a logistic model is finding the best fitting (yet biologically reasonable) model to describe the relationship between the dichotomous characteristic of interest (dependent variable or outcome variable) and a set of independent (predictor) variables. Logistic regression generates the coefficients (and its standard errors and significance levels) of a formula to predict a logit transformation of the probability of presence of the characteristic of interest.
Logit(p) = 𝛽0+ 𝛽1𝑥1+ 𝛽2𝑥2… + 𝛽𝑘, 𝑥𝑘 Logit(P) can be transformed back to p by the following formula:
- When one binary variable and one independent variable is included:
P(Y) = 1
1+𝑒−(𝛽0+𝛽1𝑥1)
When one binary variable and several independent variable is included in the study:
P(Y)= 𝑒𝛽0+𝛽1𝑥1+𝛽2𝑥2…+𝛽𝑛,𝑥𝑛 1+ 𝑒𝛽0+𝛽1𝑥1+𝛽2𝑥2…+𝛽𝑛,𝑥𝑛
where, P(Y) is probability of Y occurring, e is natural logarithm base (e≈2.71828), 𝛽0 is interception at y-axis, 𝛽𝑛 is regression slope coefficient of 𝑥𝑛, 𝑎𝑛𝑑 𝑥𝑛 is a predictor or independent variable that predicts the probability of Y.
P(Y) = 𝑒𝛽0+𝛽1𝐺𝐷+𝛽2𝑀𝑆+𝛽3𝐴𝐺+ 𝛽4𝐸𝐷𝑈+𝛽5𝐹𝑀𝐿+𝛽6𝐸𝑆+𝛽7𝐸𝑆+𝛽8𝐶𝑇+𝛽9𝐴𝐿𝑃+𝛽10𝑁𝐴𝐿+𝛽11𝐿𝑆 𝛽0+𝛽1𝐺𝐷+𝛽2𝑀𝑆+𝛽3𝐴𝐺+ 𝛽4𝐸𝐷𝑈+𝛽5𝐹𝑀𝐿+𝛽6𝐸𝑆+𝛽7𝐸𝑆+𝛽8𝐶𝑇+𝛽9𝐴𝐿𝑃+𝛽10𝑁𝐴𝐿+𝛽11𝐿𝑆