New Contributor
Posts: 2

# Log odds attribution to each independent variable

Hi,

I have some basic doubts regarding converting probabilities to credit scores.

I have gone through the formula which SAS EM scorecard node uses (given by Naeem Siddique) to convert probability to a

credit score Score = Offset+ Factor*ln(odds). In the book he uses a WOE based logistic model to assign scores to each attribute of

the categorical variable.

But let us suppose I build a logistic model with one categorical independent variable which has 3 levels using effect coding. So I

will get the equation Y = Int+beta1*level1+beta2*level2 (assuming level3 as my reference level).

In case I use the above method how can I get odds for each attribute and in turn convert them to sores. Is it that for level1 the

log odds is Int+beta1 and for level2 Int+beta2 and for reference level it is Int-Beta1-Beta2.

If so can these log odds of each category be plugged into score equation to convert them to credit scores??

Thanks,

Hari

Community Manager
Posts: 587

## Re: Log odds attribution to each independent variable

I have moved this inquiry to the SAS Data Mining Community, where it will have greater visibility with experts who can help. Thank you for using SAS Online Communities!

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Bev Brown
Super Contributor
Posts: 337

## Re: Log odds attribution to each independent variable

Hey Hari,

I recommend you to read the section for SAS Credit Scoring on the Reference Help. Press F1 on Enterprise Miner and scroll down.

The sections for Interactive Grouping and Scorecard nodes walk you through the binning and the logistic regression for the WOE of your binned variables.

Please let me know if I can help!

Thanks,

Miguel

New Contributor
Posts: 2

## Re: Log odds attribution to each independent variable

Hi Miguel,

I completely understand what is being done by scoredcard node. My question is more regarding using WOE as independent variable vis-a-vis using the original binned variable.

Let us assume i have a variable age which has been binned into 3 levels. If i use WOE of age as independent variable my equation will be Y = Int+ Beta*WOE_Age. Once i get this I could then multiply the beta with WOE for each level of age to get score for each level. Their is a formula for assigning score given my Naeem Siddique which is pretty clear.

But what if I used my original binned age variable? Then my equation would be Y = Int + Beta1*Dummy_age1 + Beta2*Dummy_age2 (assuming level 3 as reference level). In this case how will i attribute score for each level if i use Score = Offset+ Factor*ln(odds) formula. Especially what will be the score for the reference level of my categorical variable?

Let me know if my above question lacks clarity.

Thanks,

Hari

Super Contributor
Posts: 337

## Re: Log odds attribution to each independent variable

Thanks for clarifying.

The points are scaled in a similar fashion. As you mention, the main difference is whether you have a Beta for the whole binned variable, or a Beta for each of the groups.

If you want to see it for yourself, you can compare the two methods in your Scorecard node. Change Analysis variables from WOE (default) to Groups.

I hope this helps!

-Miguel

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