Stata automatically omits all posiitve or all negative outcomes during Poisson panel fixed effects regression

Question

I am trying to run a Poisson fixed panel effects regression using xtpoisson in Stata where my outcome variable is binary. For a majority of my units, the outcome is 0 for the entire duration of my panel. However, when I run 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 xtreg there is no such problem.

How do I make the xtpoisson regression work without Stata automatically omitting my units with my outcomes equal to 0. I understand that in a fixed effect regression, the regression will automatically drop all regressors which have constant values in a panel. However, I don't get why this is the case for an outcome. For instance, if my outcome is whether someone is infected dInfected, then Stata basically drops everyone who is not infected at all for the duration for the panel. But the values of the regressors that yields a not infected outcome are still of interest to me.

Answer 1

With fixed effects you base your conclusions only on comparisons within a unit. If unit does not change, then in many nonlinear models that unit adds nothing, and should thus be ignored. This is the trade-off that comes with fixed effects regressions: on the one hand you are more likely to compare like with like, on the other hand you throw away all the information you could have gotten from comparing across units. So, the problem is not Stata but your choice of using a fixed effects model.

Answer 2

In a binary or Poisson outcome you can't have negative values. This means that when the total $Y_{i\cdot}$ is zero, every outcome $Y_{it}$ must necessarily also be zero; we don't learn anything by observing that $Y_{it}$ are all zero. Since zero is the lowest possible value of the mean, zeroes can be explained by a low (large negative) value of the linear predictor and thus a low (large negative) fixed effect for the unit. When you condition on $Y_{i\cdot}$, that unit does not contribute to the conditional likelihood.

Linear models are different because (a) negative values are possible and (b) there is a variance parameter to estimate. Seeing that $Y_{it}=0$ doesn't imply the linear predictor is very negative; it suggests the linear predictor is somewhere in the vicinity of zero. That's informative about the regression coefficients. Seeing repeated zeroes also suggests that the residual variance is small. So, all-zero units are informative for both the regression parameters and the variance parameter and don't drop out of the calculation.