# Should all parameter coeffiecients be negative for WOE in logistic

I am currently Modeling fraud where the event that fraud occurs is a 0. I am using weight of evidence

A statement was made that all of the parameter coefficients must be negative for the logistic regression regardless of whether the explanatory variable positively or negatively correlates with the event of fraud. Some of the binary indicators increase risk and others decrease it.

Should all of my parameter coefficients be negative? Regardless of there influence on the response?

## 1 Answer

Certainly not.

Suppose you have a predictor $p$ with a coefficient estimate of $\hat{\beta}$ in your logistic regression. If you flip the sign on this predictor, i.e., include $-p$ instead of $p$ in the logistic regression, the estimated parameter will also flip signs to $-\hat{\beta}$.

The signs of estimated coefficients depend on the encoding of the predictors.

Whoever made that statement likely misunderstood something. If you want to make them happy, simply flip the signs on all regressors that have positive estimated coefficients. (Or better yet, educate them.)

• Oh just the director of credit policy!!!!!!!!!!!! Thanks for your response! I can see how if you change the signs you will also flip the sign on the parameter coefficient. In this case all of the risk indicators that given they are one increase fraud have a negative slope for the WOE and given that when they are 1 decrease the chance of fraud have a positive slope for the WOE. Coded this way I believe that they should all have negative parameter coefficients. – Flufylobster Sep 29 '16 at 15:13