# For Probability of Default in retail credit what is more popular logistic regression or GLM with Poisson distribution and why?

Trying to understand which regression model is more popular in retail credit card industry Logistic regression or GLM with Poisson distribution and why?

"One of the attractive features of the logistic function is the fact that it is bounded between 0 and 1, making it suitable to represent probabilities. "

"The Poisson intensity model introduced in this article still has serious shortcomings despite the major advancement offered by its dynamic features. First, it is known to be unable to properly capture the clustered default phenomenon such as is documented in Das et al. (2007). Another limitation is that the time aggregation to different horizons is easy in principle but difficult in reality. The Poisson intensity is a known function of common risk factors and individual firm attributes. For time aggregation to get to a longer horizon of interest, one must prescribe the dynamic processes for all these variables whose future values are unknown. The dimension of the dyna"

etc

http://rmi.nus.edu.sg/gcr/files/04%20GCR%20vol%201.pdf

In the credit modelling industry is more popular the use of the logistic regression with respect to the Poisson one.

This is for several reasons. Here I listed the main ones:

1) The Logistic regression is empirically shown to be better in describing that kind of phaenomenona in terms of forecasting performances and predictive capacity (try to compare the performance ratio for both of them: Accuracy ratio, ROC,...).

2) The Logistic regression suffers less the overdispersion problem that is a features of the Poisson regression models and only sometimes can be solved by using a Bivariate regression model, as, for instance, in the health care industry analysis case.

3) The Logistic regression is simpler to be implemented with respect to both the programming point of view and a theoretical point of view.

This is as regards the estimation of the probability of default. In other cases, this could be not completely true.

I suggest you to read Categorical Data Analysis by Agresti, to have a more deepen knowledge of this topic (from an econometric point of view) and, moreover, to try to test which model is better; generally, it is as above, but it depends on the economic cycle, data sample,... etc.

http://jgscott.github.io/SDS325H_Spring2015/files/logit_poisson_cox.pdf

Based on my understanding from reading the above document, I think it could be because Poisson is used for count data and Logistic is used for categorical data and we have a categorical data while doing Probability of Default (PD) modelling.