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Questions tagged [poisson-regression]

Poisson regression is one of a number of regression models for dependent variables that are counts (non-negative integers). A more general model is negative binomial regression. Both have numerous variants.

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Multiple poisson regression with one count and one continuous IV?

As one of my independent variables is a continuous variable and the other is a count variable, would I still be able to do a multiple Poisson regression?
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How much dispersion is too much for quasipoisson regression?

Quasipoisson regression goes beyond standard poisson regression in taking into account overdispersion (whereby the dependent variable's variance is much greater than its mean). This is explained at ...
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Regression strategies for predicting a binomially distributed, count outcome: Poisson, Negative Binomial, and Logistic Models with Offsets

Data Description: I am working with a dataset of 100 hens, represented across four columns: ID: Numbers 1 through 100. Age: Each hen's age. EggCount: Number of eggs laid per hen, with a range from 0 ...
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Relating animal sightings with land cover - poisson, negative binomial, zero inflated and then LOST

I have a number of sightings of animals in a location (an island). The sightings are opportunistic (corpses people stumble upon) and happen in different land covers. I am supposed to investigate if ...
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Interpreting coefficients in Log-linear model vs. Poisson regression model

I am trying to understand the difference in interpreting coefficients between log-linear regression and Poisson regression models. To clarify, when I use the term "log-linear regression", I ...
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Negative log-likelihood, high BIC, high R-squared, low error, using a difference-in-differences (DiD) methodology [closed]

I am trying to see the impact of Brexit on UK imports. My dependent variable are EU exports to the rest of world. I have monthly data from 2013 to 2023, also data is in billions of GBP. When I do ...
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Poisson regression given multiple predictors on a repeating ID variable

I was wondering how a poisson regression would work given my dataset which describes a series of zip codes stratified by age groups, gender and death counts. The regression would use death counts as ...
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Underdispersion handled with negative binomial distribution? [duplicate]

To get a more flexible model than Poisson regression, one can choose the negative binomial distribution instead for modeling with $E[y] = \mu$ and $Var(y) = \mu + \frac{1}{ \theta} \mu^2$. As a ...
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getting incidence rates from IRR using zero-inflated poisson regression

my data looks like this: and so i used zero-inflated poisson regression model to model events (e.g., hospitalization for a specific condition). ...
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My mixed poisson regression shows cross-effects between blocks. How do I report this?

I am analyzing salivary biomarker concentrations from pigs in three blocks. The saliva was taken at three sampling points(variable Time), and I have four treatments. My fixed/main effects are ...
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Why is there little difference in glm fit using poisson and gaussian family for Poisson data?

I have been puzzling over a toy regression problem with simulated Poisson distributed data and hoping someone more educated in statistics can help me gain some insight about the following observation. ...
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How to model heterogenenous count data?

I have been trying different models to model highly variable count data (mean 8.5, variance 144.3), that is grouped by participant (each participant took between 4 and 16 tests). Within each ...
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What is special about the Poisson/Binomial distributions such that they have special regression estimation techniques?

You can use maximum likelihood estimation to estimate the regression parameters for a random variable with Poisson or Binomial distributions, but I haven't heard of a chi-squared regression or a Gamma ...
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Continuous mixture distribution

I am currently working on the derivation of the negative binomial distribution as a result of a continuous mixture of Poisson and Gamma distribution for regression purposes. To obtain the entire ...
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Dealing with Underdispersion in Poisson Regression (GLM) with count data as a response variable

Related to glm() in R, I am working with count data (number of mammal species on islands) and following statistical theory, I have fitted a ...
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How to perform conditional poisson regression for a 1:5 matched cohort study?

I have a matched cohort population using data that spans the years 2016-2021. My exposure of interest is continuous dialysis treatment, and my outcome is e.coli infections (count outcome). Each time ...
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Counterintuitive phenomenon in a Poisson regression

I am trying to perform a simulation for Poisson regression. I generated X1,X2 from $\mathcal{N}(0,1)$, and then set $\lambda=0.5X1-0.3X2$. After that, I generated $Y$ from a Poisson distribution with $...
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How might I go about analyzing the affect that the number of attempts of something has on the failure rate?

I have a dataset where I know the number of attempts and number of failures for a large group of individuals. I have calculated the failure rate of each and I suspect that as there are more attempts ...
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In the mgcv ::bam function in R, how can I constrain a two dimensional smooth to be monotonically increasing in both dimensions for large data?

I have a large dataset (1.3M rows) where I want to ensure that both Age and Duration increase monotonically for each by factor level (Male, Female). Here is the setup of the model: ...
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Poor RMSEA/Fit for Simple Poisson Regression

I am running a simple Poisson regression. $X$ = time, $Y$ = count data. This is a huge dataset with many years. There is significance between $X$ and $Y$. But model shows poor fit via high RMSEA value....
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Interpretation of interaction term in log-linear models

Given the model: $\log(y) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_1 x_2$ Which can be for example a Poisson or a Negative Binomial model ($y$ would be a count variable) or a logistic ...
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Why is an offset needed in Poisson Regression? [duplicate]

Why does Poisson Regression require an offset variable when we model rates instead of a count? In a Poisson Distribution, lambda itself is a rate (e.g. cars per minute). It seems like the Poisson ...
Uk rain troll's user avatar
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Application of robust Poisson regression

I am applying a Poisson regression with robust standard errors to model a binary response variables. I was wondering what are the assumptions underlying this type of regression? Does robust Poisson ...
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logistic regression vs poisson rate regression

I have some confusion about logistic regression, Poisson regression and Poisson rate regression and I hoping to get some answers that can clear the cobwebs in my mind regarding this confusion. My ...
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Evaluating differences in Risk Ratio [duplicate]

If I have two risk ratios (calculated from Poisson regression) and 95% confidence intervals for each ratio, can I make the claim that the risk ratios are significantly different if there is no overlap ...
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Predictors of Poisson or Negative Binomial Regression of LMM or GLMM

Just wondered if statistically it is wrong to have count data as a predictor (not confounders) of a Poisson or Negative Binomial Regression of LMM or GLMM? So far, I have seen continuous or ...
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Warning: Hauck-Donner effect detected in the following estimate(s): INTERCEPT

This is a quick question because I could not find an answer online. I ran a truncated Poisson model and I got the warning in the title (perfect separation?) affecting my intercept. The output is: <...
Giovanna's user avatar
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Can I claim that the relative risk of age effect in Poisson regression is a mortality rate?

Suppose I run a poisson regression with yearly death count as outcome: $\log \mu_{t}=a + \beta_{ti} \kappa_{ti} + offset$ $\mu_{t}$ refers to the number of death at time $t$; $a$ refers to intercept; $...
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Comparing results from Poisson regressions

I have a dataset with count data (y variable), one primary variable of interest (factor denoted x_1), and several variables I wish to control for (factor and numeric denoted x_i). Say, y is the number ...
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Error metric for regression of count data: Poisson Deviance or Mean Square Error?

I would like to understand what difference it makes, if I use, for example, either Mean Square Error or Poisson Deviance as error metric/loss function for a regression of count data. Are there any a-...
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When is it appropriate to use a zero-inflated Poisson regression model?

Is it appropriate to employ a zero-inflated Poisson regression model for datasets characterized by a notable presence of zeros, even when these zeros are true zeros?
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Dependent variables are count variable with an upper bound

I need to test some hypotheses for a social sciences dissertation. In my description below, I refer to the independent as the Xs and the dependent variables as the Ys. I am expecting a straight linear ...
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How to interpret interaction coefficients in a truncated poisson

I'm working with a truncated poisson (also known as positive poisson) and I want to interpret the coefficient interaction between two variables. From this question, we see that the interpretation of ...
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How to predict average Y from averages of X for GLM Quasi-poisson regression?

Need some help from the community :) Data and Task Description I have the data in following form: Y X1 X2 0 1000 10 2 1500 200 1 1000 110 Y - is the target variable I'm trying to predict. That is ...
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Why not always use covariate instead of offset in Poisson Regression? [duplicate]

I've just started studying Poisson regression and came across the two models: $$ \begin{align*} \log{\mathbb{E}(count)} &= \beta_0 + \beta_1x_1 + \beta_2x_2 + \log(T) \\\\ \log{\mathbb{E}(count)} &...
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What is the appropriate normalization for finding correlations between Poisson distributions? [closed]

I am interested in using this algorithm, glm-pca, to find a lower dimensional embedding in time series data, specifically neuronal spiking data, which is Poisson distributed. I have looked at some ...
Angus Campbell's user avatar
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Why aren't residuals in Poisson regression on the scale of the response variable?

I am running models in R using an OLS as well as using a GLM with a Poisson distribution and log link function. ...
Amadou Kone's user avatar
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3 answers
262 views

Poisson regression for rare events?

Poisson regression is commonly used to analyse count data. However, when we deal with rare events it does not seem to be appropriate any more. At least, graphical criteria to assess the model fit like ...
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How to compute a poisson regression zero truncated and one inflated

I'm working with data of trips per tour, with tours as various trips that a person makes consecutively. I'm trying to model this with count models. My dependent variable is Number of trips per tour, ...
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Modelling count data with variable upper bound

I have been unable to find references to understand how count data can be modeled where each count observation has an unknown upper bound lying in a particular range. Let's consider the following ...
medium-dimensional's user avatar
2 votes
1 answer
101 views

What type of regression to use when outcome is integers from 0 to 10

I have an outcome variable that measures "community perception," with responses ranging from $0$ to $10$. For instance, the outcome variable might represent answers to the question: "In ...
Carlos Ramos's user avatar
8 votes
2 answers
141 views

How can I use a variable as a covariate which exists only for specific range for some clusters/groups?

I want to know how to use Poisson GLMMs when we have unequal samples available for different groups/clusters/participants in data. Imagine a study where each of the 60 participants are given 1000 ...
medium-dimensional's user avatar
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Why do the standardized beta values and CIs of a glm poisson regression model not differ from the unstandardized ones (using report function)?

For a specific research question i fitted a generalized linear mixed model using a poisson link function due to the characteristics of my data. For reporting purposes i used the report package and the ...
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Mixture of two Poisson distributions

I would like to determine the mixing between two Poisson distribution means. I have $N$ observations that are drawn from two Poisson distributions. Each observation is drawn from one of the two ...
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Comparing Age-Adjusted Mortality Rate between 2 groups

Context: I am using national mortality database to compare the mortality of X disease by demographic factors. I divided the county based on social vulnerability scoring into 4 groups (1,2,3,4 based on ...
OlgaSan's user avatar
5 votes
2 answers
215 views

GLM (Poisson regression) and Linearity

I understand that an assumption of Poisson regression is a linear relationship between the transformed expected response in terms of the link function and the explanatory variables. Therefore you ...
Randomname's user avatar
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Is it possible to estimate the cumulative effect without using distributed lag model?

I am fitting the temperature and mortality data by using conditional Poisson regression. The following formula and data are used: https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-...
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Predictive Modeling of Overseas Filipino Workers' Average Length of Stay: A Comparison of Linear and Poisson Regression Models

i want to find our average length of stay in months with a discrete values however the number of months in the dataset is up to 60 that we can treat as continuous. I would like to determine when is ...
JOENIELYN SALVADOR's user avatar
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Is there a way to set an exposure for a Poisson loss in Catboost?

I'd like to use Catboost for actuarial models (eg claims frequency). Although I see that Poisson loss is an option, I don't see that exposures are directly supported. How do people deal with this?
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Do all GLM models not require equal variance?

I am trying to learn about generalized linear models (GLMs). For example, in a Poisson GLM: $\text{g}(\mu_i) = \text{log}(\mu_i) = \beta_0 + \beta_1*X1_i$ $E[Y_i|X_i] = \mu_i = \text{exp}(\beta_0 + \...
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