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2

Why are my estimated coefficients different? They should be different. You're no longer modeling count data. You're modeling rates. The offset is just like any other predictor in a linear model, the coefficients of the other terms shouldn't change when it is uncorrelated. No. The offset is not your typical covariate. The offset is a predictor whose ...

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What you are referring to is a homogeneous or stationary Poisson process. In that case, the distribution of the waiting time (the difference between the time of the next event and the current time, $T_{\text{next event}}- T_{\text{current}}$), is independent of the current time P(T_{\text{next event}} \leq t| T_{\text{current}}) = 1 - e^{-\lambda (t- T_{\...

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What you have at hand is panel data ; fixed effect Poisson models is well understood* and can be easily applied in many statistical software. For Stata see xtpoisson ; for R, it seems that glmer() in the lme4 package with family=Poisson do it** ; or the fixest packages***. *: https://en.wikipedia.org/wiki/Fixed-effect_Poisson_model **: https://www.stata....

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This can happen if your software back-transforms the estimates before computing the intervals, and then uses the SEs of the back-transformed estimates (usually obtained by the delta method). You can avoid this by computing the intervals on the link scale (e.g., log), and then back-transforming the endpoints.

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