# Log odds to score relationship goals

### Monitoring relationship between score and odds in a propensity scorecard - ePrints Soton

In logistic regression, we have the logit β1 is the change in log odds comparing men to women .. Goals. Predict Phys (no physician visit within the past two years=1) with centered age-physician visit relationship? internal bank variables if the customer already has a relationship with the bank. In absence of a specialized application score – the generic bureau score using extensive analysis to identify the Odds or Bad rate at score bands. be centred at the mean/median point – done for illustration purpose only). Credit Scoring is a statistical method for evaluating risk of a loan applicant. in that the logit-transformed prediction probability is a linear function of the predictor computed for this purpose evaluate the improved odds for differentiating the . capable of representing any relationship between predictors and outcomes, and .

Bad Credit has been observed; however, there are likely another significant number of previous applicants, that had been rejected and for whom final "credit performance" was never observed. The question is, how to include those previous applicants in the modeling, in order to make the predictive model more accurate and robust and less biasedand applicable also to those individuals. This is of particular importance when the criteria for the decision whether or not to extend credit need to be loosened, in order to attract and extend credit to more applicants.

This can for example happen during a severe economic downturn, affecting many people and placing their overall financial well being into a condition that would not qualify them as acceptable credit risk using older criteria.

In short, if nobody were to qualify for credit any more, then the institutions extending credits would be out of business.

So it is often critically important to make predictions about observations with specific predictor values that were essentially outside the range of what would have been previously considered, and consequently is unavailable and has not been observed in the training data where the actual outcomes are recorded. There are a number of approaches that have been suggested on how to include previously rejected applicants for credit in the model building step, in order to make the model more broadly applicable to those applicants as well.

In short, these methods come down to systematically extrapolating from the actual observed data, often by deliberately introducing biases and assumptions about the expected loan outcome, had the in actuality not observed applicant been accepted for credit.

Model Evaluation Once a logistic regression model has been built based on a training data set, next the validity of the model needs to be assessed in an independent holdout or testing sample, for exactly the same reasons and using the same methods as is typically done in most predictive modeling. All of these methods, graphs, and statistics that are typically computed for this purpose evaluate the improved odds for differentiating the Good Credit applicants from the Bad Credit applicants in the holdout sample, compared to simply guessing or some other methods for making the decision to extend or deny credit.

Useful graphs include the lift chartKolmogorov Smirnov chart, and other ways to assess the predictive power of the model. For example, the following graphs shows the Kolmogorov Smirnov KS graph for a credit scorecard model. In this graph, the X axis shows the credit score values sumsand the Y axis denotes the cumulative proportions of observations in each outcome class Good Credit vs.

Bad Credit in the hold-out sample. The further apart are the two lines, the greater is the degree of differentiation between the Good Credit and Bad Credit cases in the hold-out sample, and thus, the better more accurate is the model.

### What does "20/ln(2)" mean in logistic regression? - Cross Validated

Determining Score Cutoffs Once a good logistic regression model has been finalized and evaluated, the decision has to be made where to put the cutoff values for extending or denying credit or where more information should be requested from the applicant to support the application. The most straightforward way to do this is to take as a cutoff the point at which the greatest separation between Good Credit and Bad Credit cases is observed in the hold-out sample, and thus can be expected.

However, many other considerations typically enter into this decision. First, default on a large amount of credit is worse than on a small amount of credit. Generally, the loss or profit associated with the 4 possible outcomes correctly predicting Good Credit, correctly predicting Bad Credit, incorrectly predicting Good Credit, incorrectly predicting Bad Credit needs to be taken into consideration, and the cutoff should be selected to maximize the profit based on the model predictions of risk.

There are a number of methods and specific graphs that are typically prepared and consulted to decide on final score cutoffs, all of which deal with assessing the expected gains and losses with different cut off values. Monitoring the Score Card, Population Stability, Score Card Performance, and Vintage Analysis Delinquency Reports Finally, once a score card has been finalized and is being used to extend credit, it obviously needs to be monitored carefully to verify the expected performance.

Fundamentally, three things can change: First, the population of applicants may change with respect to the important used in the score card predictors. For example, the applicant pool may become younger, or may show fewer assets than the applicant pool described in the training data from which the score card was built. This will obviously change the proportion of applicants for credit who will be acceptable given the current scorecardand this may well change where the best score cutoff should be set.

So-called population stability reports are used to capture and track changes in the population of applications the composition of the applicant pool with respect to the predictors.

## What is the best way to convert probability of default into a risk score ranging from 0-1000 ?

Second, the predictions from the scorecard may become increasingly inaccurate. The intercept of Using the odds we calculated above for males, we can confirm this: The coefficient for female is the log of odds ratio between the female group and male group: So we can get the odds ratio by exponentiating the coefficient for female.

Most statistical packages display both the raw regression coefficients and the exponentiated coefficients for logistic regression models. The table below is created by Stata. In other words, the odds of being in an honors class when the math score is zero is exp These odds are very low, but if we look at the distribution of the variable math, we will see that no one in the sample has math score lower than In fact, all the test scores in the data set were standardized around mean of 50 and standard deviation of So the intercept in this model corresponds to the log odds of being in an honors class when math is at the hypothetical value of zero.

How do we interpret the coefficient for math?

### FAQ: How do I interpret odds ratios in logistic regression?

The coefficient and intercept estimates give us the following equation: We will use We can examine the effect of a one-unit increase in math score. Taking the difference of the two equations, we have the following: We can say now that the coefficient for math is the difference in the log odds.

In other words, for a one-unit increase in the math score, the expected change in log odds is. Can we translate this change in log odds to the change in odds? Recall that logarithm converts multiplication and division to addition and subtraction. Its inverse, the exponentiation converts addition and subtraction back to multiplication and division.

If we exponentiate both sides of our last equation, we have the following: Logistic regression with multiple predictor variables and no interaction terms In general, we can have multiple predictor variables in a logistic regression model. Each exponentiated coefficient is the ratio of two odds, or the change in odds in the multiplicative scale for a unit increase in the corresponding predictor variable holding other variables at certain value.

Or is there an underlying variable at play here? Ice cream leads to murder and running the football leads to victory A commonly used example of the correlation-causation fallacy concerns ice cream sales and the murder rate. When ice cream sales rise, there is a corresponding increase in the murder rate. But ice cream doesn't promote homicidal tendencies, and committing a murder doesn't induce cravings for a triple scoop waffle cone as far as I know.

The actual cause is warmer weather, which leads to both ice cream sales and higher crime including murder. See below for an illustration.

Another example, perhaps more appropriate to this blog, would be the correlation between rushing attempts and victory in the NFL.

There is no doubt that there is a strong and persistent correlation between the number of rushing attempts a team has in a game and the likelihood of victory. See below for average win percentage by rushing attempts for the past 10 seasons of the NFL: Yards are the raw currency for points and wins in the NFL.

Why would a less efficient play lead to victory? The answer, of course, is that it doesn't. Rushing the ball doesn't lead to victory. Instead, they are both the result of building an early lead. A team with a lead particularly late in the game will tend to rush the ball more because it takes more time off the clock. Once, again, in flowchart form: Mis-matched matches Returning now to the goal frequency graph, is it possible that there is a bias in the results that is distorting the outcome?

**StatQuest: Odds and Log(Odds), Clearly Explained!!!**

Each soccer match is not a coin flip, and will feature teams with varying degrees of talent and skill.