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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Transformation of confidence limits of Poisson Log linear glmm

I fitted a Poisson log linear model of the form Y ~ poisson(lambda) log(lambda) = mu + beta1X1 + beta2X2 I obtained the estimates and confidence limits ...
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Interpreting estimates in a Poisson regression

I know similar questions have already been answered but in this particular case I need some additional help. I am working with this data set: https://github.com/proback/BeyondMLR/blob/master/data/...
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Why do results differ with and without offset in Poisson regression?

I have a dataset with counts of preterm births for five years by county. I am running analyses to see whether contaminant water concentration levels for each county for each year predict preterm ...
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Use offset variable instead of modelling y as a proportion

Most questions regarding using offset variable relates to rate or take the count per unit time. I would like to model the number of daily hospital admission (general ward, ICU etc.) from emergency ...
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GLM to use for non-negative real data or percentage data?

I would like to do a regression model for the following responses/dependent variable: number of cases at the hospital emergency department waiting time from registration to consultation percentage of ...
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Independence models in sampling 2 way contingency table?

I have just went through a lecture on sampling 2-way contingency table data via multinomial, product multinomial and Poisson sampling. The associated reduced models for each sampling are the ...
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Can IWeights Be Used as a Substitute for AWeights When Using XTPOISSON in Stata?

I am using a Poisson-regression fixed-effect model to estimate the effect that automatic voter registration had on the number of new Oregon voters in the 2016 general election. Since Stata does not ...
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How do I tell if word frequencies are changing over time?

I have a collection of texts that span about 1000 years. I am interested in the frequency of a particular word in these texts. Specifically, I want to know whether the frequency of the word increased ...
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Question about regression using a rate vs a count as the dependent variable

Let's say I wanted to run a regression of mortality on an x variable, so I could see 3 different possibilities I can do I define a rate: $y = \left(\frac{\#deaths}{population}\right)$ and regress $$...
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GLMM, repeated measures count data and Poisson regression: not positive definite, scaling, and convergence issues

Summary Using the lme4::glmer package I am trying to run a Poisson regression model with fixed effect, random intercept, and random slope. I have watched many tutorials and it seemed like this was ...
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Choosing reasonable priors for Poisson GLMM

I am using the package brms in R to fit a generalized linear mixed model using a Poisson distribution with log link. The model takes count data that ranges from 0 ...
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How to graphically diagnose conditional zero-inflation in count response regression?

Is there any ubiquitous (or not so much) graphical method in count response models (e.g. Poisson GLM) to diagnose conditional zero-inflation? I'm aware of statistical tests that can be used for that, ...
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Constant-information scale transformation

I was recently introduced to the concept of constant information scale transformations in the book Generalized Linear Model with Examples in R, by Dunn and Smyth. With that, they mention in the book ...
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Help on determining the effect of a drug in tumor counts in a within subject design

Thank you all in advance, I am having difficulties in deciding the best way to determine the effect of a treatment from observational data (there are no RCTs available). I have an observational cohort ...
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Test for equality between two regression coefficients with an interaction term

I’d like to test for equality between two regression coefficients, one of which is an interaction term. I’ve been referencing Andrew P. Wheelers statistics blog: https://andrewpwheeler.com/2016/10/19/...
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Will usual tests state that data is overdispersed if response mean in poisson regression can vary greatly?

Assume I have 1000 responses from some count data, where each response follows the Poisson distribution with a mean (and variance) falling somewhere in the large range of 1 - 100. There is one ...
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Relative risk of interaction in Poisson regression model

I have fitted a poisson regression model for the problem: "How does the number of hours spent in an emergency room, revenue of the doctor and special training of the doctor influence the number ...
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Marginal effects model with ggpredict() for a generalized poisson linear model

I am working with count data of mosquito abundance and I want to isolate the effect of land-use from the effect of topographic variables. Therefore, I'm combining a poission regression model with ...
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Regression with a fuzzy nominal predictor

I am looking at count + offset (rate) data that can be grouped into historical periods, but the borders between the periods are fuzzy, as in the specific year that delineates one period from another ...
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Why AIC for log-linear model in glm returns Inf?

I am trying to calculate the AIC for log-linear model in R, but i get Inf as a result. The model aim is to predict sales in euros based on some variables. As far as ...
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How come a Poisson GLMM predicts a higher overdispersion than in the observed data?

I am using package brms in R to fit a Bayesian generalized linear mixed model in which: the response variable is the count of a phenotypic structure (e.g., toes) ...
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Count-Response Data Example/Conditions under which Poisson GLM clearly beats Gaussian GLM in terms of Point Prediction

I've been applying both the classic linear regression (AKA "Gaussian GLM") and Poisson GLM (along with Zero-Inflated Poisson) to several count-response data examples, but I'm yet to see ...
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Forecasting count data after fitting a Poisson regression model

I have created a Poisson regression model in Python for predicting the number of orders a company will receive a day based on a dataset of order counts and a number (~5) factors that contribute to ...
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Error Terms Poisson Distributed

When might error terms be Poisson distributed? I would assume that error terms for Poisson regression will be Poisson distributed. But I could be wrong. I am just guessing. What do you guys make of ...
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Are there any difference between irr (Incidence Rate Ratio) and exp (beta) coefficient?

I am wondering that are there any difference between IRR (Incidence Rate Ratio) and the exp(beta) coefficient?
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Correct distribution to model proportion of time in a day

I would like to determine how the presence of researchers influenced the amount of time that shorebirds spent on the nest in a day. My data consists of proportions that range from 0.715-0.997, which ...
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MASS::glmmPQL diagnostic

I am fitting models with MASS::glmmPQL of the form ...
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Poisson approximation of cox

A quick (and possibly silly) question I was hoping to get some help with. I am trying to approximate a cox model using a Poisson glm. I split the follow-up time to intervals following a similar ...
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I am trying to model Y by X where Y is count data using a quasipoisson model. It doesn't seem to be fitting the data well

The data structure is that Y is count data and x is a continuous variable. Here is scatterplot of my data and the quasi-poisson model fit overlayed. I attempted two model fits - quasipoisson with the <...
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Appropriate model for amount of statistical errors in articles

I recently started my PhD and I am currently working on a project about finding statistical reporting errors. Our work is similar to Nuijten et al. (2016) only for economics. So, I have a database ...
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How can we put in firm & time fixed effects in zero inflated count model in R?

I am running a zero-inflated count data model where my dependent variable is a count variable and my independent variable is a continuous variable. Since I have plenty of structural zeros in my data, ...
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Error in Gamma Ray data: chi square value

I have Gamma-ray data for which I am fitting the stars with a constant (one parameter) first to remove the unwanted or garbage data. I plotted counts vs MJD value. For this data as Poisson, the error ...
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Standard deviation/variance for the sum, product and quotient of two Poisson distributions

What would be the standard deviation for $A+B$, $AB$ and $\frac{A}{B}$ for $A$ and $B$ Poisson distributed?
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How to correct for unequal observation time in poisson regression

So I have data from a number of people on the number of sexual partners they've had in their life so far (self reported, but let's assume they're perfectly accurate for this question). I wanted to see ...
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Why did the inclusion of random effect drastically change the parameter estimates

I working on a project using Poisson model with an offset term. Points to note: The structure of the data is such that; data were collected at state level for each year starting from 2010 to 2015. ...
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Why do we choose exponential function as the nonlinearity in Possion GLM

In Poisson GLM, the response variable $Y$ follows the Poisson distribution $$P(Y=y)=\lambda^y\exp(-\lambda)/y!$$ and: $$\lambda=\exp(\bf \theta^Tx)$$ My question is why do we use exponential as the ...
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If outcome is a count from a finite number of possible instances, is binomial or poisson regression more appropriate?

I have an outcome variable that is the number of criteria participants meet for a diagnosis of substance dependence. The minimum number of criteria participants can meet is 0 and the maximum is 11. So ...
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How to do a ppml regression with fixed effects

I am estimating a gravity model aiming at evaluating how patents can affect trade patterns. I am using a ppml model using the glm command in R. As identification strategy, I am using fixed effects ...
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Interpreting results from a Poisson and Quasipoisson model

I used Poisson regression model to model how count of user actions on a website (dependent variable) are explained by website content (independent variables). The dependent variable distribution is ...
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Negative infinity produced when computing log-likelihood in Poisson Regression R

I am trying to compute the log-likelihood in a Poisson regression in R. However, my computation produces negative infinity values for some observations. This is my code: ...
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Crude incidence rate ratios giving different results to conditional Poisson regression model

I am analysing the treatment effect of a compound, namely the rate at which an event occurs during treatment. I have calculated the crude incidence rate ratio for a group of subjects, each of whom has ...
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Basic R-Squared in Poisson Regression

I have read one cannot/should not calculate the basic R-Squared used in linear regression for a Poisson generalized linear regression model. It is logical to me that one cannot determine the basic R-...
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Why can we use a deviance test for a quasi likelihood models?

I know that the reason why you don't obtain a value for AIC if you fit a quasi-likelihood model is because a quasi-likelihood is not a real likelihood, and to obtain a value for AIC, you need a real ...
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Interpreting Poisson regression analysis

I ran my data through R and got these results. I wanted to ask about the meaning of the results. Could it be that one variable is not significant when looking at the entire model, but significant when ...
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38 views

Negative Binomial or Poisson regression?

My dependent variable (count) shows signs of overdispersion (mean 2.50, Variance 6.60), which led me to use a negative binomial model. This seems to fit better compared to the Poisson regression (...
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Testing for endogeneity in a negative binomial model

I'm trying to fit a negative binomial model to my data because the dependent variable exhibits overdispersion. However, one of my reviewers is insisting that I also test for endogeneity. He or she is ...
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How can a relationship be U-shaped when both linear and quadratic terms are positive and significant?

I have a predictor variable that ranges between 0-1, transformed to natural log due to multicollinearity and modeled with fixed effect negative binomial. Both the linear (B=9.9, St Error = 2.71, p<...
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What are the model assumptions for a poisson mixed effects model?

tldr; Aside from equidispersion, what are the model assumptions I should be checking for in a poisson mixed effects model that has a random intercept, group mean centered transformations of its ...
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What is the direct consequence of excess zeros/inflated data?

In many books and articles I've read that in a presence of many zeros in count data (correct measurement, for example "0 sales on Tuesday") we should go for hurdle or zero-inflated models. I'm ...

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