I have a dataset with a categorical target ($y$) and multiple categorical features ($x_1$, $x_2$, ..., $x_i$). I have been able to successfully use a logistic regression model to calculate an odds ratio for each feature individual.
I was wondering what metric is traditionally used for groups of categorical features together. The idea would be that the $x$ values can be split into separate groups, as in Group A ($x_1$, $x_2$, $x_3$), Group B ($x_4$, $x_5$, $x_6$), etc.
My goal is to find some statistical tool to compare the combined predictive power for the $x_i$ features together within each group. Alternatively, my $y$ values are also available as a continuous variable, so I would be grateful for any suggestions given a continuous $y$, not just a categorical $y$. The odds ratio might be the wrong analogy here, and I might be looking for something completely different. Regression might not be the right tool either.