When should I balance my data for GLM/GAM? I'm running GLMs and GAMs and I can't find a clear answer about if I should be balancing my data or not.
I'm trying to get useful descriptive models, not predictive models. So I haven't split my data into training and test. Two reasons, I didn't think that was necessary (since it isn't a predictive model) and I don't have a huge amount of data to begin with (200 samples for males, 100 samples for females). I'm investigating what factors (10) impact mortality after heart failure.
For some factors I have a massive imbalance. For example, I've separated the data on sex and 97% of females are non-smokers.
Would be it best to just omit this variable or do I attempt some balancing techniques? Do I leave it alone since it may just be representative of the real-world? From what I've read, balancing data means the model may no longer reflect reality. But in the case of the female smokers, it seems I just do not have enough data to see whether smoking impacts mortality after heart failure in females.
I wanted to apply a confusion matrix but I'm not predicting, so it doesn't seem applicable.

I would strongly suggest to avoid rebalancing your data at first instance.
Especially when using a GLM/GAM to describe the tendencies of the sample at hand it makes little sense to try to up- or down-sample the original sample as this would immediately change the base-rates. GLM/GAM predictions are generally "well-calibrated" (i.e. there are accurate as probabilities estimated by the model) and resampling with destroy the intercept ($\beta_0$) that anchor our estimates.
We might want to use some re-sampling techniques (e.g. bootstrapping) to better inform our audience for aspects of sampling variance and finite-sample precision but that's a different point.
Similarly if we care about predictive performance more, using regularisation (e.g. a ridge regression model) might be preferable, but again not a necessity for a "descriptive model"). Please note that, yes, it is perfectly reasonable to be worried about certain covariates having small absolute counts but that uncertainty will be captured by the resampling and/or the standard error associated with that coefficient.
