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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41 views

Why we cannot use linear regression with count data?

We know the counting data can use the Poisson regression or NB regression model, we also know the counting data will violate the normal distribution hypothesis when using Linear regression. I would ...
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Is aggregated poisson-distributed data still poisson-distributed?

I want to aggregate a dataset which is Poisson-distributed in which each event that occurs is measured at a different time. The data is transformed into transactional data, aggregated on UserID. So ...
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Does the inclusion of a model offset convert predictor variables from counts to rates?

Does the inclusion of a model offset in Poisson or logistic regression convert predictor variables from counts to rates? Or does it only convert response variables from counts to rates? I understand ...
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51 views

Determine statistical difference of slopes of quadratic relationship in a Poisson regression

I'm looking for a statistical or mathematical way to test the difference between two slopes. Others have asked related questions but my problem is quite particular. I'm running a Poisson regression ...
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Assess quality of a Poisson regression model on R

we did a Poisson regression because we figured out that our data are count data. Could you kindly explain us where we have to look at in order to understand the quality of our Poisson regression? ...
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Extension of Lee-Carter model with parametric functions of age and time

A standard model of mortality is the Lee-Carter model where Deaths at age $x$ and time $t$ are given by $D_{xt}\sim Poisson(E_{xt}\mu{xt})$. $E_{xt}$ and $\mu_{xt}$ are, respectively, the average ...
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The difference between residuals(XX) and XX$residuals of glm(y~x, family=poisson(link=log)) in R [migrated]

I'm executing the following program glm(y~x, family=poisson(link=log)). I can't understand the difference between residuals(XX) ...
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28 views

Admissions per year before and after antibiotics?

I need to compare hospital admissions per year before and after the introduction of antibiotics in 100 patients (antibiotics introduced at various time points in the past). Eg. Before antibiotics: ...
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Choosing the right model: Poisson, Quasi-Poisson and Negative Binomial?

[Edit] I am working in R. I am investigating the effects of weather on restaurant demand. My DV is the number of restaurant visitors per hour, my IVs are five weather variables and all other ...
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38 views

Confidence Limit for Inference on Ratios

I need to know how to construct a confidence interval on a Ratio which is the number of Incidents per Vehicle, calculated as shown for a schematic example in the image below. As shown in the image, I ...
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14 views

Does effect modification make sense for Poisson regression?

One of investigators I am working with wants to know whether the effect of an exposure on the outcome differs between two groups. She suggested throwing in interaction terms into our Poisson model. I ...
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Why does adding an offset change the coefficients in a Poisson regression?

Suppose I run Poisson regressions but every time the only difference is the offset. Why are my estimated coefficients different? The offset is just like any other predictor in a linear model, the ...
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Could this variable be modeled by a poisson regression?

I have a pc experiment and an ordered response variable with 8 levels (from 0 to 7). I have also a factor (different types of stimuli) to include as a predictor in the model. So in each trial, the ...
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76 views

My colleague wants to control for 1000 variables?

My colleague wants to make inference claims while controlling for 1000 variables. I can't seem to agree with him. How would you approach this simple example? Imagine if Ebay sold a visibility product ...
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Why are Poisson regression coefficients biased?

Suppose I run a simple Poisson regression, where $$Y \sim \text{Pois} (5X) $$ If I run a Poisson regression of $Y$ on $X$, I am expecting to get back $5$. Instead I get numbers much higher. Why is ...
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79 views

Use the offset or use rates as dependent variable in Poisson regression

I'm using a data set of an insurance company, and I want to model the number of claims (counts) as a dependent variable (number of insurance claims, nb_sinistre in this data set). In R I use a glm ...
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28 views

Interpretation of higher coefficient for group with smaller mean

I am running a fixed effects poisson model with robust standard errors in STATA (xtpqml). The model I run it on has my count data as dependent variable and then as my independent variable I have a ...
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Information about independent variables in poisson regression

Can independent variables in Poisson model, Negative binomial model and Hurdles model be categorical ?
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48 views

Frisch-Waugh-Lovell Theorem for Poisson Regression

Consider the Poisson regression model $$ Y=\exp\left( X_{1}\beta_{1}+X_{2}\beta_{2} +\varepsilon \right). $$ Is there something like the Frisch-Waugh-Lovell theorem for this model that would allow me ...
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Is the poisson regression model the best method for my data?

I'm trying to understand if restrictive firearm legislation and socioeconomic characteristics influence the movement of illicit firearms between states in the US (ATF Trace Data, 2012-2017; RAND State ...
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Unadjusted rates vs. observed rates?

In poisson and negative binomial rate models, should the observed rate be the same as the unadjusted rate (in model with only 1 variable)? Should you report these unadjusted rates from a model with ...
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Find significant neighborhoods with increase or decrease in #CurrentVisits compared to #BeforeVisits

I am currently researching on some patients data to understand the effect of a hospital's inauguration over the current visits of the patients compared to their Before visits. The study area contains ...
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Count Analysis - How to analyze the Impact of a Predictor

Say you have data as shown below and the data represents Incidents of a certain type at a Toll Plaza. The incident count is directly related to the Vehicles Per Day (VPD), so you can calculate the ...
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Estimating datapoint from log-likelihood function evaluations

Imagine that we are given multiple evaluations of a likelihood function on a datapoint for several samples of model parameters (coming from their prior), and this datapoint is hidden from us. Under ...
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Poisson regression with custom offset and link

I have the following model $$Y \sim \operatorname{Poisson}\left(\frac{1}{1+\exp(\beta X)} E\right)$$ In other words, I have count data for Poisson process with exposure E and rate given by the ...
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Does it make sense to infer a rate (as a probability distribution or upper limits) for a Poisson process if there are “no events”

I have an inhomogeneous Poisson process with a rate $\lambda (\mathbf{t})$ defined on some parameters $\mathbf{t}$. I am trying to infer $\lambda (\mathbf{t})$ from some data, which are events (really ...
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Why and how do poisson regression and negative binomial regression preserve sum of predicted outcomes

I am using poisson regression and negative binomial regression to fit a dataset. In the meantime, I discovered that the sum of fitted values of poisson regression is exactly the same as the sum of ...
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29 views

Poisson regression for count data that is not Poisson distributed?

Is it true that Poisson regression is used to model count data? But not all count data follow a Poisson distribution? Then you can still use Poisson regression in that case?
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What is the impact of excess zeros on poisson regression coefficient estimates?

The background I have a dataset with some zeros - based on how I segment my data, it is either 50% of the observations or 80% of the observations. The data is not actually count data, but from what i ...
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40 views

Is an offset term necessary for a count model of a behavior where subjects determine trial length?

We are modeling data from a behavioral study in which subject pairs' conversations are coded for specific types of utterances (say "Type A"). Subjects decide when their trial is over and we count Type ...
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34 views

Feasibility of running mixed-effects poisson/logistic regression with correlation structure such as AR(1), Toeplitz

I'm not aware of any R package that lets me use specify the covariance pattern model such as in the package nlme and run the mixed effects poisson/logistic ...
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GEE logit / Poisson versus mixed effects Poisson / logit

There's a way to do Poisson or logit mixed effects and Poisson or logit GEE in R. What's the difference between GEE and the mixed effects models for Poisson / logistic regression? I heard its the ...
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Dealing with NAs in Poisson Regression estimators [duplicate]

I am trying to fit a Poisson regression in some soccer matches. I want to be able to predict matches of the first league for a new season, which means that there will be some new teams that have been ...
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Wrong sign of a model coefficient in Bayesian Poisson-Lognormal Car model

I am trying to develop a multivariate Poisson lognormal CAR model. One of my most important variables in the model is providing a negative sign which should be positive. However, when I develop a ...
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What do I do when my model prediction exceeds the limit of 100%?

I have plotted the effects of a model glm( A ~ B, family=poisson, data=data) both with the sjplot R package and with the ...
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50 views

Why do negative binomial regression coefficients differ by level of data stratification and coefficients from Poisson models do not?

I'm trying to understand why regression coefficients from negative binomial models are sensitive to the level of stratification of the data and regression coefficients from Poisson models are not. ...
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Is Poisson regression a good fit for this dataset?

I am using a hurricane dataset (specifically the NDAM and Gender_MF columns): ...
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39 views

Poisson regression: Is a skewed Likert-scale dataset a valid candidate for this approach?

Goal My goal is to correctly model the effect of three independent variables (job autonomy, trait plasticity, and job complexity) on a dependent variable (job stress). Problem Having run a ...
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count data model with capped response variable

I'm trying to predict the total number of Olympic medals won by a country in the summer Olympics games. I have data from 2000 to 2012 relating to the country gdp, population, number of athletes sent, ...
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References: CI interval for preimage of Poisson mean

Looking for references or where to look to be able to deal with the following. Suppose I have some count data $(X_i)_{i=1}^{z}$, such that each $X_i$ is independent and Poisson distributed with mean $...
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Reporting estimates and confidence intervals for levels of categorical variable when word count is limited

I have the following (fictitious) output from a Poisson model (count ~ AgeGroup + other variables): ...
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Log-linear model for contingency table with no fixed count

I have table of counts of born children with four two-level factor variables (mother smoker/nonsmoker, child born dead/alive, ..). I would like to use log-linear model to understand interactions of ...
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Literature request: (in)appropriateness of negative binomial for count data with an upper bound

I conducted an analysis where I used binomial logistic regression to analyze x successes in n trials (where n varies between observations) in aggregate (using the R syntax ...
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340 views

The AIC for my Poisson Regression is INF. Does it mean i shouldn't use Poisson regression for my model?

I am trying to create a regression model for this variable (Y) based on 2 categorical variables. So, I created dummy variables to replace them. These dummy ...
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Predicting vector of counts

I was wondering if there are any models that are similar to Poisson regression, but instead of having 1 count as the target, there is a vector of counts as the target. For example: Typical Poisson ...
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40 views

Overdispersed poisson-distribution and offset --> standard errors?

I am modeling count data using R and doing a fixed-effects/random-effects model and thus limited on functions and therefore cannot use a quasipoisson model or negative binomial distribution, but ...
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48 views

How to choose best multiple regression model (Poisson/quasipoisson/negative binomial)? - R

I'm creating some multiple regression models on some national statistic data checking whether there is a divide in infant deaths between the north and sound of the UK. I have created models for males,...
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Exposure in Poisson regression [duplicate]

Could somebody explain the concept of exposure in the context of Poisson regression and how it relates to the expected value of a Poisson distributed response?
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What type of data is needed for offset in a Poisson regression model - R

I am trying to do a Poisson regression using the following data, where infant deaths are shown per year for both North and South England. ...
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poisson regressions simple and effects regressions (using glmer using glm) producing different result with the same data

I'm using poisson regressions to analyze count data. I have two groups of patients in a clinical trial, and I'm comparing numbers of brain lesions that can be detected on their MRIs at 3 different ...