In this article, I try to perform a set of analysis on publicly available data set, and try to build an appropriate model to predict whether a user who applied for credit card at an online bank, should be approved or not. We will solve this as we are working in company and the report needs to be submitted.

#### reading the data set ####data = pd.read_csv('case_study_data.csv')

data.head()

#### checking null values in any of the columns ####print(mi.bar(data.iloc[:,0:11], figsize = (15,5)))

`print(mi.bar(data.iloc[:,11:], figsize = (15,5)))`

One of the columns (asset_class_cd) as only 20% non null values. Since, this number is way below the rule of thumb of 40%, we will not attempt to impute the values. If the number would have been closer to 40%, we would have created a predictive model to first predict the values of asset_class_cd and then use the predicted values to run the overall model. inquiry_purpose_code has about 3% null values. asset_code alos has some null values. We will check of they are distributed completely at random and if yes, we can remove them directly as it won’t lead to reduction of large number of data points.

### removing the column ###mod_data = data.drop(["asset_class_cd"], axis = 1)

mod_data.head(10)

Visually checking if other columns that are missing data, are missing it at random or is there a pattern to null values.

`mi.matrix(mod_data)`

There is no clear pattern in the missing data and hence, we can directly remove null values, and since, there proportion of Null values are not that high so as to loose a large chunk of the data.

`mod_data = mod_data[~pd.isna(mod_data['inquiry_purpose_code'])]`

mod_data = mod_data[~pd.isna(mod_data['asset_code'])]

# Exploratory Data Analysis

We have the address data but it’s not usable in this current form. We can take zipcode out of it and try to use that in our analysis. Geographical location is can create biases in the data or may actually give sign whether the particular user will default or not.

`mod_data['zipcode'] = list(("").join(list(i)[-5:]) for i in list(mod_data['address']))`

We can extract the domain name from the email address. That might be one of the factors which can help us in predicting whether to approve or reject a user.

## if the domain name is not one of gmail, yahoo or hotmail, it's marked as others ##mod_data['domain'] = list(re.search(r"(.*)@(.*)\.", i).group(2) for i in list(mod_data['email']))

mod_data['domain'] = list(i if i in ["gmail", "yahoo", "hotmail"] else "other" for i in list(mod_data['domain']))

We have the date of birth. From the date of birth, we can calculate the current age of the user.

### converting the dob column in required column ###mod_data['date_of_birth'] = list(pd.to_datetime(i, format = "%d/%m/%y") for i in list(mod_data['date_of_birth']))

current_date = date(2022, 1, 25)mod_data['age'] = list(((current_date - datetime.date(i)).days)/365 for i in list(mod_data['date_of_birth']))### in some case, years like 1956 are being changed to 2056 ###

### taking care of that issue ###

mod_data['age'] = list(i if i >= 0 else i+100 for i in list(mod_data['age']))

We will low look at the data set summary

## description of the data frame ##mod_data.describe()

`sns.pairplot(mod_data)`

Checking if all user_id’s are unique

uni = mod_data.drop_duplicates(['user_id'], keep = "first")len(list(uni.index)) == len(list(mod_data.index))

Checking the correlation matrix

`mod_data.corr()`

we can’t see clear pattern for particular variable transformations from the above chart.

`mod_data.groupby(['approved'])['approved'].count()`

`sns.histplot(x = "age", hue = "approved", data = mod_data)`

It is clear from the above graph that users who are older are more likely to get approved.

`ax = sns.factorplot(x='education_level', y='age', hue='approved', data=mod_data, kind='bar')`

ax.set_xticklabels(rotation=65, horizontalalignment='right')

From the above graph too, it is clear that in each education level, users who get approved are on average has a higher age.

`ax = sns.factorplot(x='hours_per_week', y='age', hue='approved', data=mod_data, kind='point')`

ax.set_xticklabels(label = None, rotation=65, horizontalalignment='right')

ax.set(xticklabels=[])

`ax = sns.factorplot(x='marital_status', y='age', hue='approved', data=mod_data, kind='point')`

ax.set_xticklabels(label = None, rotation=65, horizontalalignment='right')

Both approved and disapproved rates are higher in people who have atleast been married once (regardless of their current status). This may point towards human biases that might come into play while making such decisions.

`ax = sns.factorplot(x='capital_gain', y='capital_loss', hue='approved', data=mod_data, kind='point')`

ax.set_xticklabels(label = None, rotation=65, horizontalalignment='right')

ax.set(xticklabels=[])

We want to now look at outliers and try to remove as many as we can so that it doesn’t affect our predictive model.

`sns.boxplot(x = 'age', data = mod_data)`

`sns.boxplot(x = 'capital_gain', data = mod_data)`

`sns.boxplot(x = 'capital_loss', data = mod_data)`

`sns.boxplot(x = 'hours_per_week', data = mod_data)`

`sns.histplot(x = 'domain', data = mod_data)`

`sns.histplot(x = 'education_num', data = mod_data, hue = "approved")`

`ax = sns.histplot(x = 'education_level', data = mod_data, hue = "approved")`

ax.set_xticklabels(mod_data['education_level'].unique(),rotation = 90)

`ax = sns.factorplot(y='capital_gain', x='education_level', hue='approved', data=mod_data, kind='point')`

ax.set_xticklabels(label = None, rotation=65, horizontalalignment='right')

From the above exploratory plots, we can infer the effect of age, education and other features in data vary for different users. We can also observe the outliers from the box plots and since the number of data points are not too high, we will remove them.

## Feature scaling

mod_original = mod_data.copy(deep = True)

dupl_mod_data = mod_data.copy(deep=True)mod_data['age'] = (mod_data['age']-mod_data['age'].mean())/mod_data['age'].std()mod_data['capital_gain'] = (mod_data['capital_gain']-mod_data['capital_gain'].mean())/mod_data['capital_gain'].std()mod_data['capital_loss'] = (mod_data['capital_loss']-mod_data['capital_loss'].mean())/mod_data['capital_loss'].std()mod_data['hours_per_week'] = (mod_data['hours_per_week']-mod_data['hours_per_week'].mean())/mod_data['hours_per_week'].std()### changing Gender to 1 and 0 ###mod_data['gender'] = list(1 if i == "Male" else 0 for i in list(mod_data['gender']))

## Feature importance

A lot of ML models are hard to interpret and it is difficult to gauge the importance of each parameter in the model. To make the process of interpretation much easier, we will use a game theory library called Shapley Value Explanations. SHAP is used to provide a marginal importance numberto each paramter based on their importance. I am using the same model in my research to isolate important features.

# creating dummy variables for all the string variables so that they can be used in evaluating SHAP values ##workclass = pd.get_dummies(mod_data['workclass'], drop_first = True)

education_level = pd.get_dummies(mod_data['education_level'], drop_first = True)marital_status = pd.get_dummies(mod_data['marital_status'], drop_first = True)occupation = pd.get_dummies(mod_data['occupation'], drop_first = True)relationship = pd.get_dummies(mod_data['relationship'], drop_first = True)inquiry_purpose_code = pd.get_dummies(mod_data['inquiry_purpose_code'], drop_first = True)

institute_type = pd.get_dummies(mod_data['institute_type'], drop_first = True)account_type = pd.get_dummies(mod_data['account_type'], drop_first = True)asset_code = pd.get_dummies(mod_data['asset_code'], drop_first = True)portfolio_type = pd.get_dummies(mod_data['portfolio_type'], drop_first = True)domain = pd.get_dummies(mod_data['domain'], drop_first = True)mod_data.drop(['workclass', 'education_level', 'marital_status', 'occupation', 'relationship','inquiry_purpose_code', 'institute_type', 'account_type', 'asset_code', 'portfolio_type', 'domain'], axis = 1, inplace = True)mod_data = pd.concat([mod_data, workclass, education_level, occupation,relationship, inquiry_purpose_code, institute_type,

account_type, asset_code, portfolio_type, domain], axis = 1)part_data = mod_dataX = mod_data.loc[:, mod_data.columns != 'approved']

X = X.loc[:, X.columns != 'user_id']

X = X.loc[:, X.columns != 'email']

X = X.loc[:, X.columns != 'zipcode']

X = X.loc[:, X.columns != 'date_of_birth']

X = X.loc[:, X.columns != 'address']

Y = mod_data['approved']X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.20)masker = shap.maskers.Independent(data = X_test)model = LogisticRegression(random_state=1, max_iter=1000).fit(X_train, y_train.values.ravel())explainer = shap.LinearExplainer(model, masker=masker)

shap_values = explainer(X_test)shap.plots.beeswarm(shap_values)

From the above chart it is clear that relationships, education_num, marital_status, age, capital gains play the most major role in deciding what features to include. We will go from there and add variables in sort of forward step wise regression, i.e. once a variable has been added to the model, it will not be removed.

Starting from the four features above, we will do forward regression to come to our best model.

formula = 'approved ~ age + education_num + capital_gain + C(inquiry_purpose_code) + C(relationship) + C(occupation) + C(institute_type) + C(marital_status)'

fit = smf.mnlogit(formula=formula, data=dupl_mod_data).fit()

print(fit.summary())print("AIC =", str(fit.aic))

`AIC = 25571.174263297573`

Now, that we have our linear regression model, we will check the if there is any multicolinearity.

## calculating vif for quantitative variables ##y, X = dmatrices('approved ~ age + education_num + capital_gain + capital_loss', data=dupl_mod_data, return_type='dataframe')#calculate VIF for each explanatory variablevif = pd.DataFrame()

vif['VIF'] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]

vif['variable'] = X.columns

vif

Since all the vif values are around 1, we can safely assume that there is no multicolinearity in the dataset among quantitative variables.

# Business Problem

I think, since we are working with mobile only bank, their business relies on their credit card customers not defaulting and hence, I believe from the data set, true negative is more important than true positive or the overall accuracy. The higher we can have true negative, the higher are the chances that we will be able to catch an user and not approve their credit card.

## dividing the dataz_columns = ['approved','age', 'education_num','capital_gain', 'relationship', 'occupation', 'institute_type', 'inquiry_purpose_code', 'marital_status']part_data = dupl_mod_data[z_columns]X = part_data.loc[:,part_data.columns != 'approved']

Y = part_data['approved']X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.20)X_train, X_val, y_train, y_val = train_test_split(X_train, y_train, test_size = 0.2)XY_train = pd.concat([X_train, y_train], axis=1, join='inner')formula = 'approved ~ age + education_num + capital_gain + C(inquiry_purpose_code) + C(relationship) + C(occupation) + C(institute_type) + C(marital_status)'fit = smf.mnlogit(formula=formula, data=XY_train).fit()

fit.summary()### using the validation set to find the optimized threshold value ####true_negative = []

true_positive = []

threshold = []

expected = list(y_val)

predict = list(fit.predict(X_val)[1])for i in list(np.linspace(0, 1, 100)):

predicted = list(1 if j > i else 0 for j in predict)

cm = confusion_matrix(expected, predicted)TP = cm[0][0]

FN = cm[0][1]

FP = cm[1][0]

TN = cm[1][1]

#print(TP, FN, FP, TN)

# Specificity or true negative rate

TNR = TN/(TN+FP)

TPR = TP/(TP+FN)

#print(TPR, TNR)

true_negative.append(TNR)

true_positive.append(TPR)

threshold.append(i)

At the threshold value of 0.2, we can see that we get the best performance for TNR and hence, we will use this value on our testing set.

expected = list(y_test)

predict = list(fit.predict(X_test)[1])predicted = list(1 if j > 0.2 else 0 for j in predict)

cm = confusion_matrix(expected, predicted)TP = cm[0][0]

FN = cm[0][1]

FP = cm[1][0]

TN = cm[1][1]

print(TP, FN, FP, TN)

# Specificity or true negative rate

TNR = TN/(TN+FP)

TPR = TP/(TP+FN)

#print(TPR, TNR)

print(TNR)

print(TPR)

From our out of sample testing, we are able to accurately predict 87.2 % of the users that we should decline. The accuracy may improve with more sophisticated models but interpretability decreases.

Since, we have only taken small number of variables, we will not worry about FDR rate. But, in case it is required, we can always use the procedure of FDR correction but that will not affect the predictive power of the model, which is our main aim in this problem statement.

We would need a person’s age, education num, capital gain, relationship status, occupation, institute type, marital status and inquiry purpose code to predict whether the user should be declined or not.

A more sophisticated algorithm or inclusion of interaction terms might gives us better results but that would be unnecessary complication in the model since we have already have a high TNR.

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