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When calculating Information Value and Weight of Evidence, it's possible to draw a chart of WoE for each variable to study its effect on the state of the target variable.

Now, I know it's possible to group values of continuous numeric variables into ranges by grouping those values with similar WoE score in the chart. However, my question is whether it is correct to group together categories of a categorical variable based on the same principle?

In this example, I used the lymphography dataset: https://archive.ics.uci.edu/ml/datasets/Lymphography

I have selected the "pathological" findings and calculated WoE of variable "changes in structure" on it, here is the resulting chart:

enter image description here

Is it alright to group "coarse", "diluted", "drop-like", "faint" and "stripped" into a single category (value)?

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If you think you can do this for bins of a continuous variable, there is no reason you cannot also do it for categories of a categorical variable! But, there are probably better strategies for model building. See for instance Principled way of collapsing categorical variables with many levels? or What is the benefit of breaking up a continuous predictor variable?.

One underlying is that when you have other variables, as you probably have, they are not used at all in your proposal. Univariate screening and such are generally not a good idea. For weight of evidence see Intuition behind Weight of Evidence and Information Value formula

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