I am constructing a credit scorecard using logistic regression, similar to the one shown here. However, when trying to convert the coefficients of logistic regression into score representation (by scaling the values using the provided formula) I am getting numbers that dont make much sense.
Formula used for calculating scores:
Score_i= (βi × WoE_i + α/n) × Factor + Offset/n
where βi is the coefficient of the logistic regression (of variable
WoE_i is the weight of evidence of corresponding variable,
α is the intercept of the logistic regression,
Factor is calculated as
PDO / ln(2),
Offset is calculated as
target_points - (factor * ln(target_odds))
n is number of variables used in regression
In my case PDO = 50, target_odds = 2, target_points = 500, n = 81, and intercept is -0.12686514.
Here is an example of one of my features:
As it can be seen, both WoE and the coefficients increase in value as the "revenue" variable increases. The score however does not act in this way. Initially I just assumed the scores acted in inverse proportion to those two values so I added a negative sign in front of the formula:
Score_i= -(βi × WoE_i + α/n) × Factor + Offset/n
But for some other features, the score is proportional to the other values:
And adding the negative sign would now make this feature have a score that does not make much sense.
How can I keep the scaling consistent? What am I doing incorrectly here?