Can Loan Default Probability Be Predicted from Personal Attributes?

In summary, the data provided includes information on individuals' sex, age, home ownership status, income, loan amount, and whether they defaulted on the loan or not. The goal is to understand the relationship between these characteristics and defaulting. The "def" variable can be considered as the response, and a logistic regression model can be fitted using the glm() function in R. The coefficients from this model can help determine the influence of each variable on the likelihood of default, and the predict() function can be used to estimate the probability of default for a specific individual.
  • #1
ghostyc
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The data here are concerned with whether people default on a loan taken from a particular bank and for identical interest rates and for a fixed period. The information on each individual is their sex (male of female); their income (in pounds), whether the person is a home owner or not, their age (in years), and the amount of the loan (in pounds).

The information recorded is whether the individal defaulted on the loan or not. Study the data and try and understand a relation between the persons characteristics and defaulting. Specifically, what is your estimated probability that a female aged 42, who is not a home owner, has an income of 23,500, and took a loan of 12,000, defaults on the loan?

The table holding the data have headings as follows:

m/f: male=1, female=0
age: age in years
home: home=1 is a home owner, home=0 is not a home owner
inc: income
loan: amount of loan
def: default=1, non-default=0.

Dataset is given in file "tabl3.txt".

I know it has something to do with Binary response and probably we should use GLM to model it. However, I kind of stuck with it. My problem is that I can do identify which variable is the response in this case.

If I use
[tex]
\log \frac{p}{1-p}=default = sex+age+income+home+loan
[/tex]
with a logit link. It just dese not make sense to me. Because "default" take on 1 or 0. So the predicted value then takes 1 or 0.

Any suggestions?

For those who knows R, here is my code.
Code: 
    Q3=read.table("tabl3.txt")
    colnames(Q3)=c("Sex","Age","Home","Inc","Loan","Def")
    Q3$Sex=as.factor(Q3$Sex)
    Q3$Home=as.factor(Q3$Home)
    Q3$Def=as.factor(Q3$Def)
    summary(Q3)

Thanks!
 

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  • #2


Hello,

Thank you for sharing your thoughts on this forum post. It is great that you are considering using a GLM to model this data. However, you are correct that the response variable in this case is not clear. Since the goal is to understand the relationship between a person's characteristics and their likelihood of defaulting on a loan, we can consider the "def" variable as the response.

To start, you can try fitting a logistic regression model using the glm() function in R. The formula would look like this:

glm(Def ~ Sex + Age + Home + Inc + Loan, data = Q3, family = binomial)

This model will give you the estimated coefficients for each variable, which can help us understand the relationship between the characteristics and defaulting. You can also use the predict() function to calculate the estimated probability of default for a specific individual, such as a female aged 42, who is not a home owner, has an income of 23,500, and took a loan of 12,000.

I hope this helps. Let me know if you have any further questions. Best of luck with your analysis!
 

Related to Can Loan Default Probability Be Predicted from Personal Attributes?

1. What is a binary response GLM model?

A binary response GLM (Generalized Linear Model) is a statistical model used to analyze data with a binary response variable, meaning a variable that can only have two possible outcomes (e.g. success or failure, yes or no). It is a type of regression model that is used to investigate the relationship between the binary response variable and one or more explanatory variables.

2. What types of data are suitable for a binary response GLM model?

A binary response GLM model is suitable for analyzing data with a binary response variable, such as categorical data, count data, or proportions. It is commonly used in fields such as biology, medicine, psychology, and social sciences.

3. How does a binary response GLM differ from a traditional linear regression model?

A binary response GLM differs from a traditional linear regression model in several ways. Firstly, it is used to model binary response variables instead of continuous response variables. Secondly, it uses a different type of link function (e.g. logit or probit) to relate the response variable to the explanatory variables. Lastly, it allows for non-normal distributions of the response variable, whereas a traditional linear regression model assumes a normal distribution.

4. What is the purpose of using a binary response GLM model?

The purpose of using a binary response GLM model is to understand the relationship between a binary response variable and one or more explanatory variables. It can help identify which explanatory variables are significant predictors of the response variable and how they influence the probability of a certain outcome. This can be useful in making predictions and understanding the factors that contribute to the outcome of interest.

5. How do you interpret the results of a binary response GLM model?

The results of a binary response GLM model can be interpreted by looking at the estimated coefficients for each explanatory variable. These coefficients indicate the direction and magnitude of the relationship between the explanatory variable and the log odds (or probability) of the binary response variable. Additionally, statistical significance tests can be used to determine if the relationship is significant. The overall model fit can also be evaluated using measures such as the deviance or the area under the ROC curve.

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