Linked Questions

0 votes
1 answer
1k views

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 ...
0 votes
0 answers
66 views

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 ...
3 votes
1 answer
295 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 ...
1 vote
1 answer
109 views

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 ...
11 votes
2 answers
9k views

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 ...
92 votes
1 answer
89k 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?
1 vote
1 answer
396 views

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 ...
4 votes
2 answers
179 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 ...
7 votes
1 answer
723 views

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 ...
8 votes
2 answers
9k views

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 ...
9 votes
1 answer
4k views

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 ...
0 votes
1 answer
3k views

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 ...
3 votes
0 answers
762 views

Can a GLM with exponential response distribution be transformed into a Poisson regression instead?

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 ...