I am trying to build a binary regression model and I will be using LASSO. The dataset is the credit card dataset where the binary response is defaulted and not defaulted. Now, I know that LASSO will shrink some of the coefficients of my variables. I have seen that some people "group" categorical variables - i.e., this makes the algorithm to either have the whole categorical variable in or completely remove it. I have a question particular for this problem and one that's generalized:
For example I have categorical variables
PayStatusMay... until June, and they each have 13 categories -
-2means there was no credit used,
-1means the person paid on time,
0means use of revolving credit, and
1means delay for one month (and so on until
9). So, would it make sense to leave just some categories of some variables? So for example take
PayStatusJune-1to be the variable which states whether the person paid duly in june. Would it make sense to include only the
-1category and exclude other ones from
PayStatusJune? Note - I am aiming not only for predictive power but also for explainability. My thinking is that if this exact category (
PayStatusJuneis indicative enough and LASSO algo leaves it in, then why would I want to include other categories from
PayStatusJuneand just make the model oversaturated with irrelevant categories. Furthermore, as for the explainability aspect of my model - leaving only one category doesn't hinder the explainability (i.e., it doesn't make the model harder to interpret)?
And the more general question:
Why would I want to group any variable, even if I want my model to be explainable?