With Delta-p statistics, the predictions based on a logistic regression model are easy to understand by non-technical decision-makers.
Learn how to calculate the Delta-p statistics based on the coefficients of a logistic regression model for credit application processing.
Data workflow includes the steps for accessing the raw data to training the logistic regression model, and evaluating the effects of individual predictor columns with Delta-p statistics.
Keep in mind logistic regression might not be the best choice when working with high dimensional data, with many correlated predictor columns.
Imagine a situation where a credit customer applies for a credit, the bank collects data about the customer – demographics, existing funds, and so on – and predicts the credit-worthiness of the customer with a machine learning model. The customer’s credit application is rejected, but the banker doesn’t know why exactly. Or, a bank wants to advertise their credits, and the target group should be those who eventually can get a credit. But who are they?
In these kinds of situations, we would prefer a model that is easy to interpret, such as the logistic regression model. The Delta-p statistics makes the interpretation of the coefficients even easier. With Delta-p statistics at hand, the banker doesn’t need a data scientist to be able to inform the customer, for example, that the credit application was rejected, because all applicants who apply credit for education purposes have a very low chance of getting a credit. The decision is justified, the customer is not personally hurt, and he or she might come back in a few years to apply for a mortgage.
In this article, we’ll explain how to calculate the Delta-p statistics based on the coefficients of a logistic regression model. We demonstrate the process from raw data to model training and model evaluation with a KNIME workflow where each intermediate step has a visual representation. However, the process could be implemented in any tool.
Assessing the Effect of a Single Predictor with the Delta-p Statistics
Logistic Regression Model
When we use the logistic regression algorithm for classification, we model the probability of the target class, for example, the probability of a bad credit rating, with a logistic function. Let’s say we have a binomial logistic regression model with a target column y, credit rating, with two classes that are represented by 0 (good credit rating) and 1 (bad credit rating). The log odds of the target class (y=1) vs. the reference class (y) is a linear combination βx of the predictor columns x (account balance, credit duration, credit purpose, etc.). A logistic function of βx transforms the log odds into a probability of the target class:
where β is the vector of coefficients for the predictor columns xin the logistic regression model that predicts the target class y.
The target and reference classes can be arbitrarily chosen. In our case, the target class is “bad credit rating,” and the reference class is “good credit rating.”
If the single predictor column xi is continuous, the coefficient βicorresponds to the change in the log odds of the target class when xi increases by 1. If xi is a binomial column, the coefficient value βi is the change in the log odds when xi changes from 0 to 1. The change in the probability of the target class is provided by the logistic function, as shown in Figure 1.
Figure 1. Logistic function modeling the probability of the target class y=1 as a function of one continuous predictor column xi
The Delta-p statistics transforms the coefficient values βi into percentage effects of single predictor columns to the probability of the target class compared to an average data point e.g., an average credit applicant.
By definition, the Delta-p statistic is a measure of the discrete change in the estimated probability of the occurrence of an outcome given a one-unit change in the independent variable of interest, with all other variables held constant at their mean values. For example, if the Delta-p value of a predictor column xi is 0.2, then a unit increase in this column (or a change from 0 to 1 in a binomial column) increases the probability of the target class by 20 %. The following formulas show how to calculate the prior and post probabilities of the target class and, finally, the Delta-p statistics as their difference1:
Use Case: The Effect of Credit Purpose and Current Account Balance on Credit Rating
Let’s now demonstrate this with an example, and check how the credit purpose and balance of an existing account improves or worsens the credit rating. We use the German credit card data provided by the UCI Machine Learning Repository. The dataset contains 21 columns that provide information about demographics and economic conditions of 1,000 credit applicants. Thirty percent of the applicants have a bad credit rating, and 70 % have a good rating. You can download the data in .data format by clicking “Data Folder” on top of the page, and selecting the “german.data” item on the next page. The german.data file can be opened in a text editor and saved, for example, in csv format. The column names and descriptions of the values in the categorical columns are provided in the german.doc file, accessible via the same “Data Folder” page.
The workflow in Figure 2 shows the process from accessing the raw data to training the logistic regression model, and evaluating the effects of individual predictor columns with Delta-p statistics. The process is divided into the following steps, each one implemented within a separate colored box: Accessing data (1), preprocessing data as required by a logistic regression model (2), training the model (3), and calculating the Delta-p statistics based on the model coefficients (4). In the preprocessing step, we convert the target column from the 1/2 notation to “bad”/“good.” We also transform two originally multinomial columns into binomial columns: We encode the “checking” column into two values “negative”/“some funds or no account” based on the status of the existing bank account. We encode the “purpose” column into values “education”/“no education” to assess the effect of education as a credit purpose. Finally, we handle missing values and normalize the numeric columns in the data.
Figure 2. The process from accessing raw credit customer data to training a credit rating model, and to evaluating the effects of predictor columns to the credit rating with Delta-p statistics. This solution was built in KNIME Analytics Platform, and the Assessing Effects of Single Predictors with Delta-p workflow can be inspected and downloaded on the KNIME Hub.
Figure 3 shows the coefficient statistics of the logistic regression model, reproducible in any tool. The “Coeff.” column shows the coefficient values for the different predictor columns, 0.683 for purpose=education. The “P>|z|” column shows the p-values of the coefficients, 0.055 for purpose=education. This means that education as a credit purpose increases the probability of a bad credit rating, since the coefficient value is positive, and this effect is significant at 90 % significance level, since the p-value is smaller than 0.1.
Figure 3. Coefficient statistics of a logistic regression model that predicts the credit rating good/bad of a credit applicant
By looking at the coefficient statistics of the logistic regression model, we find out that education as a credit purpose increases the probability of a bad credit rating compared to other credit purposes. In addition, the coefficient value 0.683 tells that the log odds ratio for getting a bad credit rating with/without education as the credit purpose is 0.683, and the odds ratio of the two groups is e0.683=1.979. What would this mean, for example, in a group of 100 credit applicants, let’s say 20 of them with education as the purpose (group 1) and the remaining 80 with another purpose (group 2)? If 10 out of the 80 applicants in the group 2 have a bad credit rating, so their odds is 0.125, then according to the odds ratio 1.979, the odds for the group 1 must be ~2 times the odds of the group 2, so 0.25 in this case. Therefore 5 (a quarter) of the applicants in the group 1 must have a bad credit rating!
The coefficient statistics have a universal scale, and we can use them to compare the magnitude and the effect of different predictor columns. However, to understand the effect of a single predictor, the Delta-p statistics provide an easier way! Let’s take a look:
In Figure 4 you can see the Delta-p statistics and the intermediate results in calculating it, also shown below for the purpose=education variable:
Figure 4. Delta-p statistics, its intermediate results, and the corresponding coefficient statistics of a logistic regression model that predicts the credit rating good/bad of a credit applicant
The value 0.159 of the Delta-p statistics indicates that education as a credit purpose increases the probability of a bad credit rating by 15.9 % compared to an average credit application.
If we wanted to compare the effect to the opposite situation, i.e., the credit purpose is not education, instead of an average credit applicant, we would need to recalculate the prior probability and also mean-center the binomial values of the predictor column of interest xi. In our data, 5 % of the people apply the credit for education purposes, so the mean of the “purpose” column xiis 0.05 .
The value 0.158 of the Delta-p statistics indicates that the credit applied for education purposes increases the probability of a bad credit rating by 15.8 % compared to those who apply it for other purposes. There’s hardly any difference to the previous situation where we compared against an average applicant and obtained the Delta-p value 0.159 (Figure 4). This means that the credit applicants with other purposes than education are very close to the sample average in terms of their credit rating, apparently because they make up 95% of the total sample.
Now we know that applying credit for education purposes has a negative effect on the credit rating. Which column could have a positive effect? Let’s check the effect of the other dummy column that we created, the “checking” column that tells if the balance of the existing account is negative. The coefficient value of checking=some funds or no account is -1.063 with a p-value 0, as you can see in the first row in Figure 3.
As the Delta-p statistics -0.171 in the first row in Figure 4 show, credit applicants with no negative account balance tend to have a 17.1 % lower probability of a bad credit rating than an average credit applicant. Interestingly, we found two columns, purpose and checking, that have an effect of almost the same size but a different direction. If we look at the odds ratio of these two variables in Figure 4, we wouldn’t get the same information at first glance: The odds ratio is 0.345 for checking=some funds or no account and 1.979 for purpose=education.
In this article, we have introduced Delta-p statistics as a straightforward way of interpreting the coefficients of a logistic regression model. With Delta-p statistics, the predictions based on a logistic regression model are easy to understand by non-technical decision-makers.
In this article, we used Delta-p statistics to assess the individual effects that make a credit application succeed or fail. Of course, the use cases of Delta-p statistics are many more. For example, we could use it to determine the individual touchpoints that decrease or increase the customer satisfaction the most, or to find the symptoms with the highest relevance, when detecting a disease. Also notice that not always the whole process from raw data to model training and model evaluation need to be completed, Delta-p statistics can also be used to re-evaluate the coefficients of a previously trained logistic regression model.
Delta-p statistics can only be used to assess the individual effects of predictor columns in a logistic regression model. Logistic regression might not be the best choice when working with high dimensional data, with many correlated predictor columns, and columns not correlated with the target column. The target classes also need to be linearly separable in the feature space.
If you want to replicate the procedure described in the article, one option is to install the open source KNIME Analytics Platform on their laptops and download the KNIME workflow attached to the article for free. A visual representation of the workflow is available on the KNIME Hub without installing KNIME Analytics Platform. Other options are to implement the calculations in any another programming tool, or even perform them manually with a calculator.
About the Authors
Maarit Widmann is a data scientist at KNIME. She started with quantitative sociology and holds her Bachelor degree in social sciences. The University of Konstanz made her drop the “social” part when she completed her Master of Science! She now communicates concepts behind data science in videos and blog articles. Follow Maarit on LinkedIn.
Alfredo Roccato is an independent consultant and trainer with a focus on data science. He studied statistics at the Catholic University in Milan and has been serving companies with business intelligence and analytics for over 35 years. Follow Alfredo on LinkedIn.
If you need extra cash and have considered applying for a loan even with a bad credit score, you might have already heard about the no credit check loan.
Image by Bermix Studio
Many people opt for a no credit check loan as their last resort. Like any other loan options, a no credit check loan has its pros and cons. Knowing if this is the best option for you allows you to go consider both its advantages and disadvantages.
But is it your best option? Is there another way to acquire cash without looking into your credit record?
Here are the other advantages of a no-credit loan:
No Credit Checks
You are considering this loan option because the lender will not bother to check your credit report. It doesn’t matter whether you have a good or a bad credit score as long as you are eligible and can comply with their requirements.
This benefit is one reason why this loan option attracts many borrowers, especially those who don’t have an impressive credit score and those who are still building their credit records.
Other loan options will require you to provide a good reason why you are acquiring the loan.
For example, lenders will ask you how you will use the loaned money aside from knowing your capability to repay the money you owe. But with the no credit check loan, lenders will ask you this kind of question during your application.
Just like any other options available out there for you, a no credit check loan also has its disadvantages. These things may be huge factors for some consumers, while to others, they’re just minor inconveniences you need to deal with.
Higher Interest Rates
One of the most common and obvious disadvantages of a no credit check loan is its higher interest rate. Since the lenders will not bother looking at your credit history and rating, they will impose a higher interest rate on your loan.
The higher interest rates imposed are due to risks they take in lending you their money without even knowing if you can pay it back. This is a common rule for all lenders who offer a no credit check loan.
Required a Minimum Loan Amount
If you only need a small amount, a no credit check loan may not be the best option for you. Lenders require a minimum loan amount when you apply for a no credit check loan. Most personal loans with no credit check will require you to loan a higher amount than other loan options such as payday loans and single-payment loans.
May Require A Collateral
Lenders may require you to have collateral as an assurance for the money you are borrowing from them. It is also to secure their part if ever you cannot pay back the cash you borrowed from them. If you default on your loan, the lender will forfeit the collateral. Collateral can be in the form of any valuable assets such as a house, vehicles, and jewelry.
Another positive thing when acquiring a personal loan with no credit check is the speedy process. You can get the money in just a few minutes or hours as long as you comply with all of their requirements and are eligible for the loan.
Reminders Before Applying for This Loan
There are things that you should watch out for when opting for this loan type, especially if you do it online, such as:
Watch Out For Fake Lenders
This is the risk associated with a no credit check loan. Some criminals use this to lure their victims for phishing and identity theft. Make sure that you choose a legitimate lender and never give out personal information prematurely. It is best to ask someone you trust for a recommendation or for help with securing a loan from a trusted lender.
Prepare The Requirements Ahead Of Time
It is best to prepare all the requirements before applying for the loan to help you acquire the money quickly. Check your chosen lender’s website or print ads for a list of requirements they will need.
Even though this loan option does not require a credit check, it does not mean you are guaranteed approval. If the lender finds out that you are not eligible for a loan, your application will be denied.
Asking yourself if a specific loan option is good for you is one of the proper ways to assess if you should apply for it or not. This practice should be observed in applying for no credit check loans and other loan types available. Remember, not all loans are suitable for you. One loan may work better for others but may not work the same for you. Hence, be prudent and choose the loan option that suits best with your financial needs.
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Dubai: Many still decide to confront bad credit card habits only after they are thousands of dirhams in debt. Here we discuss some lessons many regretted not learning before making mistakes that proved costly.
Although credit cards offer convenience, security, and rewards, overspending with a credit card and the interest and fees can bury you financially. So it’s important to know whether you possess such habits in the first place.
Four questions to ask yourself first
If you don’t know whether you have a bad credit card habit here are four questions to ask yourself to find out. If the answer to any of the below is yes, you are inching towards a credit card debtpile.
1. Do you pay only interest fees or minimum payments when you send in your credit card payment?
2. Have you ever paid your credit card late because you didn’t have the money for the payment?
3. Do you use your credit card when you don’t have enough cash?
4. When your issuer raises your credit limit, do you spend more because you can?
Bad credit card habits
While common mistakes include habitually paying your credit card late and taking out costly cash advances on your credit card, here are some uncommon-yet-dire mistakes that may slip under any user’s radar.
Habit #1: Missing out unauthorised or fraudulent charges
Keep in mind that one of the main benefits to reading your credit card statement is, it is one of the best ways to catch unauthorised charges and billing errors.
Don’t check your credit card statement for your balance and payment information, review the entire statement to verify your account activity.
By routinely checking your online or physical statement, you can also find out well before hand if your credit limit was lowered since you last checked – as it can change because of your credit habits or your credit history.
Habit #2: Paying only the minimum can cost you dearly
It is evidently easier to make the minimum payment and this is a habit credit card companies profit from as well.
Although paying just the minimum is more convenient than to figure how much extra you can pay towards your outstanding credit card bill, keep in mind that when you’re making only the minimum payment, you’re not making much progress toward paying off your credit card bill.
Moreover, unless you have a very low balance or a zero per cent interest promotion, you’re probably paying much more in finance charges than you have to.
Habit #3: Using your credit card more than your debit card
While it’s recommended you use your credit card to amass cashback rewards or points and also pay off your credit card balance every month, you shouldn’t opt to use your credit card over your debit card, if those aren’t the reasons why you would go about using them.
Your debit card is your direct access to the funds you should use for everyday purchases, like groceries, gas, clothing, and other expenses. If you use your credit card, it should be a decision with a plan for paying off what you’re charging on the card.
Habit #4: If you are transferring balances just to avoid payments
Although promotions like balance transfers are a widely recommended strategy to pay off a high-interest rate balance on your credit card, matter experts reveal that if you’re in the habit of pursuing such promotions to avoid paying payments on your credit card, this leads to amassing long-term debts.
Financial planners reiterate that many don’t realise that balance transfers typically have fees that will increase your overall balance if you’re never making payments toward the transfer. Moreover, if you’re making purchases on the card with such a promotion, the problem gets bigger.
Expert tips to take control of these credit card habits
Lesson #1: Pay your credit card in full each month
The best way to keep your credit utilisation ratio low and avoid costly interest charges is to pay your credit card balance in full each month – which also means you also don’t incur any large due.
It’s effective to control spending by not spending more than you can comfortably pay down each month, as this helps you reduce the likelihood of developing long-running credit card debt.
If you want to take in one step further, setting a monthly spending limit that’s well within your budget increases the chances that you’ll actually be able to zero out your monthly balance and avoid interest charges.
Lesson #2: Keep your credit utilisation ratio low
What it means by ‘credit utilisation ratio’ is essentially the link between your credit card balances and your aggregate spending limit. For example, a Dh2,000 balance on a credit card with a Dh5,000 credit limit equates to a 40 per cent credit utilisation ratio.
As a rule of thumb, your credit utilisation ratio shouldn’t exceed 40 per cent, and keep in mind that high ratios may adversely impact your credit score.
Financial advisors recommend aiming for a 30 per cent credit utilisation ratio, as that gives you some leeway to cover urgent one-off expenses, which can come unexpectedly as a result of maybe losing your job during the ongoing pandemic.
Lesson #3: Setting up customised spending alerts
If controlling your credit card spending is burdening you, it has been widely advised to set up customised spending alerts.
This will let you know when you’ve made an abnormally large payment or exceed a certain balance threshold and you also can pair these data alerts with security alerts to help flag any sham spending patterns.
Lesson #4: Using credit card rewards and points to your advantage
If you have a rewards credit card, you can use it to your advantage. If you have a pure cash back credit card, use any cash rewards you receive to put toward your account balance or directly deposit it into your savings account.
Alternatively, if you have a rewards points credit card, you can use your rewards to buy discounted gift cards to the stores you know, which will help save on future purchases without having to use your credit card.
If not, you could always redeem your reward points for cash redemption to put into savings or towards your account. However, ensure you know when your rewards expire to get the most out of them financially.
There’s nothing saying you can’t apply for an auto loan immediately after a repo, but the tough part is actually being able to qualify for the loan. Since many auto lenders don’t approve borrowers with a repo that’s less than a year old, you may have to consider in-house financing.
Repossessions and Your Next Car Loan
Unfortunately, most traditional auto lenders don’t work with borrowers that have a recent repo on their credit reports. When we say traditional, we’re referring to lending institutions such as banks, credit unions, online lenders, and the captive lenders of some automakers. These lenders often require a good credit score and clean credit reports.
Where does that leave you? Well, likely in-house financing is the next logical step if you need a car loan after a repossession.
More on In-House Financing
Buy here pay here (BHPH) dealerships use in-house financing. This way of auto financing involves working with the dealer who’s also your lender. There’s no need to find a third-party lender or preapproval – the dealer takes care of all that. This setup can be convenient, and often, borrowers are able to walk away with a vehicle the same day they first set foot on the lot.
Since these dealers may not check your credit reports to determine your eligibility for auto financing, your recent repossession generally isn’t an issue. If you can meet income requirements, prove you have stable work, secure auto insurance, and prove your identity, you might get into a vehicle after a repo with in-house financing.
Here are a few more details on in-house financing:
Used cars only – BHPH dealers only offer used vehicles. However, used cars are a good option for bad credit borrowers. They’re almost always less expensive than a brand-new car, and affordable is a good price when you need to get back on your feet after a repo.
Anticipate a higher interest rate – Without a credit check, lenders are taking a risk approving a car loan without knowing much about your credit history. To make up for this, they tend to assign higher interest rates. A high interest rate may be considered a good trade-off for an auto loan with bad credit in many cases, especially if you heavily rely on a vehicle to get by.
Credit repair may not be an option – If you get an auto loan with a lender that doesn’t check your credit, it’s a possibility that your on-time payments aren’t going to be reported to the credit bureaus. If you want to repair your credit with a car loan, ask the lender about their credit reporting practices before you sign on the dotted line.
Down payments are required – Few things are certain in the auto lending world, but one thing you can count on is needing a down payment if your credit is less than perfect. BHPH dealers often require a down payment of up to 20% of the vehicle’s selling price.
Prepare your documents – While a BHPH dealer may not check your credit, they’re likely to ask about your income and possibly your work history. You need proof of income to qualify for a car loan, no matter what lender you work with, so prepare at least a month of computer-generated check stubs. If you don’t have W-2 income, have copies of your last two to three years of tax returns.
Looking Forward After a Repo
After one year, your auto loan options open up a little bit more and you’re more likely to qualify for a subprime car loan. Subprime lenders are equipped to assist bad credit borrowers. These lenders offer you a chance for credit repair because they report their loans and work with poor credit borrowers.
If you need a vehicle quickly, a BHPH dealership could be your first step in getting back on the road. Once some time has passed, and your repossession loses some impact on your credit reports, you can try for an auto loan that has the potential to repair your credit.
Here at Auto Credit Express, we know a thing or two about bad credit auto loans, and we have a nationwide network of dealerships that assist bad credit borrowers. We aim to match consumers to dealers in their local area that help with credit challenges. If you’re in need of auto financing, start right now by filling out our free auto loan request form. We’ll look for a dealer in your local area at no cost and with no obligation.