I am trying to run a poisson fixed panel effects regression using xtpoisson on Stata where my outcome variable is a binary variable. For a majority of my units, the outcome variable = 0 for the entire duration of my panel. However, when I run a xtpoisson, Stata automatically omits all such units. I have the same problem when I run a xtlogit. When I run a standard fixed effect panel with there is no such problem.
How do I make the xtpoisson regression work without Stata automatically omitting my units with my outcome values equal to 0. I understand that in a fixed effect regression, the regression will automatically drop all regressors which has constant values for all values of any given unit in a panel. However, I dont get why this is the case for an outcome variable. For instance, if my outcome variable is whether or not someone is infected or not (dInfected), then Stata basically drops everyone who is not infected at all for the duration for the panel. But the value of the regressors that yields a not infected outcome, are still of interest to me.