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### When to use an offset in a Poisson regression?

Does anybody know why offset in a Poisson regression is used? What do you achieve by this?
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### Poisson xgboost with exposure

I was trying to model a count dependent variable with uneven exposure. Classical glms would use log(exposure) as offset, also gbm does, but xgboost does not allow for offset until now... Trying to ...
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### Can Weights and Offset lead to similar results in poisson regression?

In "A Practioner's guide to Generalized linear models" in paragraph 1.83 it is stated that: "In the particular case of a Poisson multiplicative GLM it can be shown that modelling claim counts with ...
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### How is a Poisson rate regression equal to a Poisson regression with corresponding offset term?

I do not understand the role of weights in "weighted Poisson regression". What exactly is being weighted? Is it the contribution of the observation to the log-likelihood of the model, or something ...
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### Predict function on negative binomial produces strange fitted values when adding an offset

I have an over-dispersed count dataset and I want to add an offset to my negative binomial on the RHS to create a rate of events for y (see this great answer for ...
115 views

### Mixed Effect Model - Roadkill hotspot v. coldspot

This problem concerns road mortality. We have 4 highway sections of varied length that were flagged as problem areas for road mortality with large mammals (moose, deer, elk, and even cows). We used ...
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### Modeling continuous abundance data with a GLM in R: how to select the correct distribution family?

I have abundance data (counts) that I have standardized by area sampled, making them continuous. I would like to explain them with my two independent variables using a GLM but I am having trouble ...
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### Poisson regression: how do number of observations and offset affect variance of betas?

Background: In Poisson regression with an offset, like in this answer, @Hong Ooi writes Your underlying random variable is still $Y$, but by dividing by $\varepsilon$ we've converted the LHS of ...
Given the following generative model $$T | \mathbf{x_i} \sim \operatorname{Exp}(\lambda_i)$$ $$\ln(\lambda_i) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \dots$$ That is: I have observations of ...