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### AIC difference after adding offset in negative binomial in R

I'm quite confused about how R calculate likelihood/AIC in glm.nb after adding the offset. In this example, the regression coefficients are the same but the AICs ...
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### How do I describe this negative binomial regression with offsets in math and words?

I've been using a negative binomial model to compare the number of particles in the ocean of different sizes to their abundance. My gam, in r code looks like this ...
192 views

### Negative-Binomial Method of moments with an offset

Given the method-of-moments approach to estimate the parameters of the NB-2 distribution $\mu$ and $\phi$: $$\mu = \bar{y}$$ $$\phi = \frac{\bar{y}^2}{s^2 -\bar{y}}$$ How can this be extended to ...
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### Best GLM to model a random variable that represents a count over a non-fixed interval of time

The random variable on which I am seeking to fit a GLM is the number of times a patient has a blood glucose level measurement above a specified threshold before they are escalated onto a stronger ...
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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 ...
82k views

### When to use an offset in a Poisson regression? [duplicate]

Does anybody know why offset in a Poisson regression is used? What do you achieve by this?
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### Should I include offset in null negative binomial model for comparing to full model?

I'm modeling how various landscape and ecological factors affect the I'd like to evaluate how well my negative binomial model performs over the null. I've specified an offset variable in my model to ...
164 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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### 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 ...
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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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### 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 ...
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 ...