Neglecting sample size, is there something that I can miss if I choose to model separately each of the levels of my categorical variable?
To be more specific, I want to predict a binary outcome $Y$ with two predictors $X$ (continuous) and $G$ (categorical, $n$ levels). I could build one logistic regression model $Y \sim X + G$ or build $n$ regressions $Y \sim X$, one for each level of $G$.
What is the risk of not pooling the data in this latter scenario?
EDIT: I forgot to mention that I have good reasons to think that pooled data is not homogeneous and it's much more homogeneous inside each group.