This is a continuation of our banking case study for scorecards development. In this part, we will discuss information value (IV) and weight of evidence. These concepts are useful for variable selection while developing credit scorecards. We will also learn how to use weight of evidence (WOE) in logistic regression modeling. The following are the links where you can find the previous three parts (Part 1), (Part 2) & (Part 3).
Experts in Expensive Suits
A couple of weeks ago I was watching this show called ‘Brain Games’ on the National Geographic Channel. In one of the segments, they had a comedian dressed up as a television news reporter. He had a whole television camera crew along with him. He was informing the people coming out of a mall in California that Texas has decided to form an independent country, not part of the United States. Additionally, while on camera he was asking for their opinion on the matter. After the initial amusement, people took him seriously and started giving their serious viewpoints. This is the phenomenon psychologists describe as ‘expert fallacy’ or obeying authority, no matter how irrational the authorities seem. Later after learning the truth, the people on this show agreed that they believed this comedian because he was in an expensive suit with a TV crew.
Nate Silver in his book The Signal and The Noise described a similar phenomenon. He analyzed the forecasts made by the panel of experts on the TV program The McLaughlin Group. The forecasts turned out to be true only in 50% cases; you could have forecasted the same by tossing a coin. We do take experts in expensive suits seriously, don’t we? These are not few-off examples. Men in suits or uniforms come in all different forms – from army generals to security personnel in malls. We take them all very seriously.
We have just discovered that rather than accept an expert’s opinion, it would be better to look at the value of the information and make decisions oneself. Let us continue with the theme and try to explore how to assign the value to information using information value and weight of evidence. Then we will create a simple logistic regression model using WOE (weight of evidence). However, before that let us recapture the case study we are working on.
Case Study Continues ..
This is a continuation of our case study on CyndiCat bank. The bank had disbursed 60816 auto loans with around 2.5% of the bad rate in the quarter between April–June 2012. We did some exploratory data analysis (EDA) using tools of data visualization in the first two parts (Part 1) & (Part 2). In the previous article, we have developed a simple logistic regression model with just age as the variable (Part 3). This time, we will continue from where we left in the previous article and use weight of evidence (WOE) for age to develop a new model. Additionally, we will also explore the predictive power of the variable (age) through information value.
Information Value (IV) and Weight of Evidence (WOE)
Information value is a very useful concept for variable selection during model building. The roots of information value, I think, are in information theory proposed by Claude Shannon. The reason for my belief is the similarity information value has with a widely used concept of entropy in information theory. Chi Square value, an extensively used measure in statistics, is a good replacement for IV (information value). However, IV is a popular and widely used measure in the industry. The reason for this is some very convenient rules of thumb for variables selection associated with IV – these are really handy as you will discover later in this article. The formula for information value is shown below.
What distribution good/bad mean will soon be clear when we will calculate IV for our case study. This is probably an opportune moment to define Weight of Evidence (WOE), which is the log component in information value.
Hence, IV can further be written as the following.
If you examine both information value and weight of evidence carefully then you will notice that both these values will break down when either the distribution good or bad goes to zero. A mathematician will hate it. The assumption, a fair one, is that this will never happen while a scorecard development because of the reasonable sample size. A word of caution, if you are developing non-standardized scorecards with smaller sample size use IV carefully.
Back to the Case Study
In the previous article, we have created coarse classes for the variable age in our case study. Now, let us calculate both information value and weight of evidence for these coarse classes.
Let us examine this table. Here, distribution of loans is the ratio of loans for a coarse class to total loans. For the group 21-30, this is 4821/60801 = 0.079. Similarly, distribution bad (DB) = 206/1522 = .135 and distribution good = 4615/59279 (DG) = 0.078. Additionally, DG-DB = 0.078 – 0.135 = – 0.057. Further, WOE = ln(0.078/0.135) = -0.553.
|Download the attached Excel to understand this calculation : Information Value (IV) and Weight of Evidence (WOE)|
Finally, component of IV for this group is (-0.057)*(-0.553) = 0.0318. Similarly, calculate the IV components for all the other coarse classes. Adding these components will produce the IV value of 0.1093 (last column of the table). Now the question is how to interpret this value of IV? The answer is the rule of thumb described below.
|Information Value||Predictive Power|
|< 0.02||useless for prediction|
|0.02 to 0.1||Weak predictor|
|0.1 to 0.3||Medium predictor|
|0.3 to 0.5||Strong predictor|
|>0.5||Suspicious or too good to be true|
Typically, variables with medium and strong predictive powers are selected for model development. However, some school of thoughts would advocate just the variables with medium IVs for a broad-based model development. Notice, the information value for age is 0.1093 hence it is barely falling in the medium predictors’ range.
Logistic Regression with Weight of Evidence (WOE)
Finally, let us create a logistic regression model with weight of evidence of the coarse classes as the value for the independent variable age. The following are the results generated through a statistical software.
|Logistic Regression Results (Age Groups and Bad Rates)|
If we estimate the value of bad rate for the age group 21-30 using the above information.
This is precisely the value we have obtained the last time (See the previous part) and is consistent with the bad rate for the group.
I wish there was an instrument similar to information value available with us to estimate the value of information coming from so called experts. However, next time when an expert on a business channel gives you the advice to buy a certain stock, take that advice with a pinch of salt.
Read the remaining part of credit scoring series
- Part 1: Data visualization for scoring
- Part 2: Creating ratio variables for better scoring
- Part 3: Logistic regression
- Part 5: Reject inference
- Part 6: Population stability index for scorecard monitoring
References 1. Credit Risk Scorecards: Developing and Implementing Intelligent Credit Scoring – Naeem Siddiqi 2. Credit Scoring for Risk Managers: The Handbook for Lenders – Elizabeth Mays and Niall Lynas