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Questions tagged [offset]

A variable with a fixed coefficient of 1. Offsets are commonly used in Poisson regression to allow the modeling of rates instead of counts.

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1answer
51k views

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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2answers
26k views

Where does the offset go in Poisson/negative binomial regression? [duplicate]

(First of all, just to confirm, an offset variable functions basically the same way in Poisson and negative binomial regression, right?) Reading about the use of an offset variable, it seems to me ...
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4answers
19k views

Using offset in binomial model to account for increased numbers of patients

Two related questions from me. I have a data frame which contains numbers of patients in one column (range 10 - 17 patients) and 0s and 1s showing whether an incident happened that day. I'm using a ...
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2answers
6k views

In a Poisson model, what is the difference between using time as a covariate or an offset?

I recently discovered how to model exposures over time using the log of (e.g.) time as an offset in a Poisson regression. I understood that the offset corresponds to having time as covariate with ...
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3answers
897 views

Using glm() as substitute for simple chi square test

I am interested in changing the null hypotheses using glm() in R. For example: ...
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2answers
6k views

Binary Models (Probit and Logit) with a Logarithmic Offset

Does anyone have a derivation of how an offset works in binary models like probit and logit? In my problem, the follow-up window can vary in length. Suppose patients get a prophylactic shot as ...
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3answers
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Should I use an offset for my Poisson GLM?

I am carrying out research to look at differences in fish density and fish species richness when using two different underwater visual census methods. My data was originally count data but then ...
9
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1answer
8k views

Predict GLM poisson with offset

I know this is probably a basic question... But I don't seem to find the answer. I'm fitting a GLM with a Poisson family, and then tried to get a look at the predictions, however the offset does seem ...
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3answers
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Modelling count data where offset variable is 0 for some observations

I'm trying to help a student of a colleague. The student observed and counted bird behaviour (number of calls) in an experimental setup. The number of calls attributable to a specific observed bird ...
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2answers
3k views

How can Poisson GLM work with non-count data (rate data)? [duplicate]

My question is related, but not the same as the following question: Fitting a Poisson GLM in R - issues with rates vs. counts Here's some fake data: ...
7
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1answer
4k views

Interpretation of intercept term in poisson model with offset and covariates

I'm using offset for the first time (as per a recommendation from a colleague) and have a couple questions about interpreting my results. Our ultimate goal is to look at the effect of some population ...
6
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1answer
9k views

How to formulate the offset of a GLM

I am trying to build a generalized linear model in R for some count data. Basically I have counted the number of animals per unit after having them presented with a treatment (for all units there was ...
6
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1answer
981 views

When to use offset() in negative binomial/poisson GLMs in R

I'm trying to detect relationships between species abundances (counts) and time (years) for many species using either Negative Binomial or Poisson regressions (depending on degree of dispersion). ...
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2answers
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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 ...
6
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1answer
664 views

R-squared value when using offset — how is it calculated?

I have a linear model with a test score variable as a dependent variable and a vector of covariates. I have an offset variable in the model. So the formula is= $$\text{score}_i = B_0 + B_xX_x + ...
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1answer
324 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 ...
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2answers
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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 ...
5
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1answer
1k views

Quasi-poisson or negative binomial regression with continuous dependent variable?

My dependent variable is originally count data. Because of several corrections it became continuous variable (originaly my data are pellet-group counts (for estimating deer density), corrected for ...
5
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1answer
507 views

Offset in Poisson regression when using an identity link function?

It appears that in Poisson regression, using an identity link function means your betas will be rate differences, and using a log link function your (exponentiated) betas will be rate ratios. You can ...
5
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1answer
4k views

Difference between offset and exposure in Poisson Regression

Exposure and offset are two techniques often used in Poisson regressions by actuaries to predict claim frequency . From my understanding, offset and exposure are the same things, so I don't ...
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1answer
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lme4: glmer problems with offset()

this is my first post, so I hope everything is in the right format. I have some problems with glmer and don't know how to fix it, so I hope somebody can help me out with this. I could not find an ...
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1answer
959 views

How to derive the Projected normal distribution

Suppose we have a bivariate normal variable $\mathbf{x}= (x_1, x_2)$ with mean $\mu_1$ and $\mu_2$ and variances $\sigma_1^2$ and $\sigma_2^2$ and correlation $\rho$. I need to obtain the pdf of the ...
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Analysis of survival data using binomial GLM with offset

We are interested in determining whether there's an association between frequency of screening visits and cancer outcomes and whether that differs by race. We have Medicare data to analyze this. ...
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1answer
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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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2answers
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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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1answer
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Predicting with GAM, using an offset

I came in a new post because I’m quite confused with the use of an offset in gam() function (mgcv package). I’m actually working on predicting marine top predator’s distribution using aerial surveys (...
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2answers
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Offset in Logistic regression: what are the typical use cases?

Offset is commonly used in Poisson regression to take into account different exposure (different time periods for instance): offset = log of exposure Question: ...
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1answer
407 views

Is it possible to use two offsets?

I am doing negative binomial linear mixed model using lme4 package in R. My question is whether or not there is a way to put two ...
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1answer
1k views

How to interpret glm and ols with offset

I ran a few glm and linear models with an offset. Each row in the dataset is a healthcare user. The data contains medical payments and icu days of each user between 2000 to 2007. As the number of ...
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1answer
3k views

Difference between: Offset and Weights?

I´d like to know the difference between these parameters when I am using GLM/GLMM/GAMLSS/BETAREG. I have observed a lot of published studies using offset, weights and covariates, however I am not sure ...
4
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1answer
495 views

Offset in Poisson regression

Consider an offset term in a Poisson regression: $$\log \mu_x = \log t_x+ \beta_0 + \beta_{1} x$$ To interpret $\beta_0$, would you need to consider $(\beta_0+ \log t_x)$? Because what if $t_x \neq ...
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1answer
55 views

Can I model incidence per 1000 people per month using poisson regression without an offset or using weights?

I am trying to model incidence rates (number of malaria cases per 1000 people per month) over time. I only have the data in the form of rates per 1000 people per month, i.e. I do not know the total ...
4
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1answer
723 views

Scaling vs Offsetting in Quasi-Poisson GLM

I recently modeled insurance claim frequency assuming a Quasi-Poisson distribution in R. My frequency dependent variable was calculated, in advance of modeling, as the number of claims per underlying ...
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2answers
934 views

Proportion as Dependent Variable or Control for the Denominator in Regression Model

I am a little confused as to which model specifications to use for my question. I have number of technological failures (positive count variable) as dependent variable but I am supposed to control ...
4
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1answer
5k views

Calculating predictions and confidence intervals from a negative binomial distribution

I'm trying to use R's glm.nb to calculate predictions and confidence intervals. When I'm using linear models after training a model, e.g., using: ...
4
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1answer
829 views

Poisson Rate Regression: Offset? [duplicate]

I'm comparing two groups on the # of hospitalizations they have in a 5 year period. Length of hospitalization stay is highly variable. For example, a patient might have 3 hospitalizations that in ...
4
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0answers
394 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 ...
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0answers
542 views

How a tweedie glm handles an offset?

I am trying to fit a model with a glm using a tweedie family. I use a index parameter p between 1 and 2 to get a compound Poisson Gamma distribution to fit my data. But I want to use an offset only on ...
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3answers
5k views

How to estimate and interpret an offset correctly in a Poisson regression?

Assume the following easy example of a glm regression with an offset: ...
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1answer
1k views

Regression trees to model rates

I am performing a predictive modeling application where I have to predict claims. If I had used classical GLMs, I would have used a poisson glm using log exposure as offset, assuming therefore $$\text{...
3
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3answers
867 views

Regression for a Rate variable in R

was tasked with developing a regression model looking at student enrollment in different programs. This is a very nice, clean data set where the enrollment counts follow a Poisson distribution well. I ...
3
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1answer
35 views

Poisson regression on devices that fail during observation period?

I am observing N devices over a period of time $[0,T]$ and counting the number of certain events $y_j$, for each device, during that period of time. I also have some specifications $x_j$ for each ...
3
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1answer
299 views

offset in logistic regression to take into account a priori individual probability estimates

I am performing a logistic regression (LR) model on a set of data on which an initial probability estimate for event occurrence, sai $\hat{p_i}^{base}$ has been provided. I have supplementary ...
3
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1answer
947 views

Offset for Negative Binomial Regression

I've constructed a Negative Binomial Regression wherein I predict the number of words an individual will find from a set of seven letters based on the average frequency of words that the set of ...
3
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1answer
219 views

Need an offset in GLMM even when it is almost invariable and an offset-free model yields a better fit?

I am analyzing frequency data (response variable = no. of seeds produced per plant) by fitting GLMM with a logarithmic link function and a Poisson error distribution. I also have data on no. of ovules ...
3
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1answer
105 views

GLM of proportions with offset

I am fitting a glm with a binomial family to consider the relationship between the proportion of trials in which courtship of a female type $A$ occurs (successes) and male genotype (a two level factor)...
3
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0answers
114 views

How does Poisson regression (with an offset) relate to Logistic regression?

I have some data I am trying to analyze of how often someone has chosen a given option (which I'll call choice A) vs not choosing it (which I'll call choice B) during a 6 month period. Each subject ...
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0answers
123 views

How can I account for different sampling effort in my GLMM Poisson regression using glmer() - easily reproduced example inc

I've been grappling with my dataset for what seems like a very long time now. Hope someone can point me in the right direction. I would like to know how to account for the differing sampling effort ...
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0answers
37 views

What does one do when the coefficient for the log of the rate estimator for a poisson rate model is very different from 1?

Let's say we have "number of accidents" as the response in a poisson regression model. One of the predictors is "number of days." Naturally, we expect more accidents to occur over more days, so it ...
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0answers
112 views

How to account for patterns in GAMM residuals due to the addition of an offset?

I have been wrestling with some model problems for a few weeks now and would like some help. I am trying to determine whether fish catch rates have changed following an event using GAMM. Because ...