Which logistic regression model should you use if the outcome variable is numerical/quantitative and discrete, e.g. days, number of readmissions, number of contacts? Normally you use linear regression to continuous outcome variables and logistic regression to binary variables. But a numerical, discrete variable is neither of those.
@Michael You can refer to statistics by Jim website and choose what regression analysis fits your data best.
https://statisticsbyjim.com/regression/choosing-regression-analysis/
Your examples point towards some count-data model approach. The Poisson and the Negative Binomial are the typical ones. The NB is less "demanding" when it comes to assumptions, and therefore in many cases the safest choice. If there at an excess number of zeros in the counts, both models have zero-inflated options to account for this.
Usually for quantitative data linear regression is often a good alternative (single or multiple linear regression)
The linear regression would be a good option for you
you can check the more details here:
https://statisticsbyjim.com/regression/choosing-regression-analysis/
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