# 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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### Poisson GLME with different observation period

I measure blinking frequency from two groups of Subjects. Each patient visit my lab several times. During each visit I measure the number of blinks during observation time. Observation time is ...
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### NLP as a Poisson Regression Problem?

Suppose I encode the sequence to sequence dataset as a vector of integer $\{0,1\cdots N\}$ where $N$ is the maximun number of unique words in the dataset. For example, I am planning to build a chatbot ...
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### Why 'residual deviance divided by the degrees of freedom is around 1' is a threshold for over-dispersed?

I have difficulties determining over-dispersed. I actually have 2 questions about it. Firstly, for Poisson regression, E(Y)=Var(Y) since we assume that Y follows Poisson distribution. Thus over-...
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### Poisson regression with time dependent covariates

I am an epidemiologist and recently our team receive a data from nursing homes in our city. We have weekly data for each elderly person for about 3 years during their stay in nursing homes. The ...
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### Mean-variance plot to visually check overdispersion in Poisson regression model

I have an estimated mean versus variance plot, as shown below. I found a vlog that uses it to visually check overdispersion (https://towardsdatascience.com/adjust-for-overdispersion-in-poisson-...
1 vote
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### WHy is the over dispersion in this poisson and quasi-poisson the same?

I have a zero inflated count data, on which I have run a poisson and quasi poisson reg using glm(). The output from a poisson model is as follows: ...
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### Biased Parameter Estimation in Poisson Regression

I read over here (https://aip.scitation.org/doi/pdf/10.1063/5.0040330) that "If the equi-dispersion is not met, the Poisson Regression is no longer appropriate to model the data. Moreover, the ...
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### Question About Overdispersion and Poisson Regression [duplicate]

I am an MBA student and taking some classes in statistics - I have taken a few basic stats classes where we learned about the fundamentals of statistics and probability. We started learning about ...
1 vote
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### How to use poisson to predict incidence rates per 100,000?

I am trying to make predictions with a poission model to get the predicted incidence rate per 100,000 of some event. My problem is that when I compare the predicted incidence to the incidence ...
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### Why Specifically Use Poisson Regression For Count Data?

I am a MBA Student that is taking some statistics courses, a colleague recommended this site as a useful resource! So far there seems to be a lot of interesting information here! I posted a previous ...
1 vote
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### Modeling Target Variable based on Days Since Last Engagement

I have a data frame of engagement data for different sites for every day like this: SITE_ID Date Engagement A Count Engagement B Count Target Variable 1 1/1/2022 0 0 1 1 1/2/2022 0 0 0 1 1/3/2022 ...
1 vote
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### Poisson Model Interrupted Time Series Analysis

I've run an Interrupted Time Series Analysis on count data, fitting a Poisson Model as below: ...
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### Negative binomial or Poisson

Using MASS::glm.nb (R) I am having problems of convergence with certain dataset, and it seems theta goes very high, resulting in NaNs "In sqrt(1/i)" during the fit. I am trying to understand ...
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### Why are outcomes from poisson regressions more precise than linear? [closed]

I'll quickly qualify what I mean by "precise": I don't mean "correct" in any way. But, I was messing around running a lot (100s) of regression models, with an outcome that behaves ...
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### How to model insurance count data with a large number of zeros and no number of claims in a period greater than 1

I have a large dataset for insurance claims and I am trying to model both the number of claims and the severity of claims based on a number of explanatory variables using a General Linear model. As is ...
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### Interpreting a Negative Binomial Regression

I've produced a negative binomial regression where the dependent variable is the number of AIDS-related laws passed by each of the US's fifty states in 1989, with the independent variable of ...
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### Should we complete missing combinations with 0 in count data?

I'm working on count data preparation which will be used in Poisson/GLM. Specifically for year 2002 both males and females rows are missing as no event has been recorded (0 counts). Therefore should I ...
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### Generalized Poisson regression using glmmTMB

I'm modelling a discrete (and naturally bounded) underdispersed variable $Y$ taking values in $0, 1,..., k$ and the aim is to estimate the conditional probabilities $P(Y ≤ y \ | \ X)$ under the model ...
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### Interpreting Over-dispersion test for Poisson regression

I did the over-dispersion test for my Poisson regression model in R, to check whether negative binominal is a better option. I used stats package for conducting ...
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### Correct variable/data use for day of week predictors [duplicate]

Currently trying to model count data using ticket counts for each day of week as the dependent variable (y) and the corresponding day of the week integrated using OHE for 78 days. Assuming Poisson ...
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### Double-count in Poisson Regression (SAS) for repeated measurement?

my team is working on a project about covid incidence in elderly nursing home in a particular state. We tried using proc genmod in SAS with link=log and dist=poisson to calculate the incidence but it ...
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### Why is my simulated Poisson regression mean not equal to the variance?

I simulated a simple poisson regression model as follows $x \sim Normal(2, 1)$ $\mu = \exp(0.6 + 0.9 x)$ $y \sim \text{Poisson}(\mu)$ ...
1 vote
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### log transforming a Poisson variable

Trying to understand how log-transforming a count variable changes the regression equation. The reason I ask is because I see a lot of researchers log-transform their data so they can use OLS. Say you ...
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### Count vs. continuous predictors in Poisson regression with offset

I'm having a conceptual problem related to using different types of predictor variables (i.e., count data vs. continuous data) in Poisson regression. My field method was walking transects and counting ...
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### Poisson distribution with a constant term

I have a set of data constituted by two columns: $Y$ with non-negative discrete values, depending on a time $t$. I make the hypothesis that $Y$ is a Poisson distribution, with: \operatorname {E} (Y\...
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### How to identify drivers of a count variable?

I have an app in which users go through a form and select options which represent their views about an event they attended. These options are presented like "tags" that the user can select. ...
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### Assumption of Poisson regression with robust standard errors

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? I understand that the ...
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### Running a poisson GLM with cyclical explanatory variable?

Im running a few poisson GLMs looking at count data of bats sightings in relation to lunar cycle. We specifically want to look at how species are affected leading up to and away from new moon/full ...
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### unstructured covariance matrices & magnitude of correlation

I am reading a paper in behavioral medicine where they want to determine if stress at time point 1 affects the chances of having a physical health condition at time point 2. At some point in the paper ...
1 vote
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### Using a log-poisson model to predict mortality

I'm trying to build a GLM in Python that uses a log-poisson model from the statsmodels package to predict mortality rates. I have a policy level dataset that, among other features, contains attained ...
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### choice between zero inflated poisson and zero inflated negative binomial

For count data with excessive number of zeros, there are two choices of models, zero inflated poisson and zero inflated negative binomial. Q1: How does one make appropriate choice between the two from ...
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### Should I use Chi-Squared or Fisher's test?

everyone. I have a question which involves statistics and the R programming language, thus I believe that this question pertains to this forum, but if any of you know someplace else where I could go ...
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### Can Poisson deviance be used to evaluate models that use loss functions other than Poisson? (Such as MSE)

I am currently doing a a study on emergency department utilization rates at various geography levels. Especially of interest, are tree-based approaches to this analysis - namely random forest and GBMs....
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### How to calculate a r-squared for a zero-truncated poisson mixed model (glmmTMB)

I am interested to calculate the pseudo-r-squuared for a zero-truncated poisson mixel model (using glmmTMB). The r.squaredglmm (package MuMin) gives a message that it can not calculate pseudo-r2 for ...
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### How do you estimate the magnitude of seasonality in time-series data?

I have some time-series data showing the monthly counts of hospital admissions. It has both a long-term trend (increasing) and seasonality (highest in summer). I am trying to measure the magnitude of ...
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### Can the Predictors be Count Variable for Logistic Regression?

I have a general question regarding logistic regression. May I know if the predictors of logistic regression (mixed effect with random variables) could be count variables (e.g., 6,10,20,21)? I ...
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### What is the distribution of the error term in the Poisson Regression model? [duplicate]

Given a Poisson regression model as $y = E(y\mid x) + ε$ where $λ = E(y\mid x) = \exp(x'β)$ with $y$ from the Poisson distribution ($\operatorname{Poisson}(λ)$) I am trying to understand the ...
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### Negative Binomial Regression Not Running in R [closed]

I’m having some issues with event count analysis in R, and I welcome any help I can get. I’ll walk through my issue as (to me) it seems rather bizarre. It starts off when I try to run a negative ...
1 vote
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### Why does Poisson regression not have a closed form solution?

I am trying to understand GLMs by trying to run them on my own on some Poisson data. My understanding is that if I have my Y values and X values, then using the log-link function, $log[Y] = mX+b$ for ...
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### How to do generalized estimating equations with zero inflated poisson regression in R?

I did not find a package to do zero inflated Poisson/negative binomial regression with generalized estimating equations. Is there such a package available? How to do generalized estimating equations ...
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### In Poisson models with an offset, should performance metrics (such as deviance) be calculated in terms of raw counts or counts per exposure?

For context, I need some metrics that can compare a standard Poisson regression (with population offset) to a random forest regressor with Poisson criterion. The test predictions for both methods are ...
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### Dependent value largely right skewed. What are my options?

I am modeling a dependent variable which is heavily right skewed by a large number of independant variables. This variable is integer. But let's assume this is our model. $Y = a_0 X_0 + a_1 X_1 + b_0$...
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### Predicting estimated time of arrival (ETA) with custom loss function

I have an assignment of ETA prediction that I'd like to seek some advice from you. I need to train a model from a dataset to predict ETA of parcels as dependent variable, which is discrete (in days). ...
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### Discrepancy in degrees of freedom from R svyglm vs glm

I fitted a Poisson model using svyglm in R. The null and residual deviances from the svyglm model are as expected. For the degrees of freedom however, I get confusing results. With a sample size of n=...
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### Is "vanilla" random forest regression appropriate when dependent variable is a rate (i.e. per 100 people)?

To add a little more context, I am working with a dataset from which I want to predict the population-normalized count of emergency department visits on county level, with 50+ independent variables. ...
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### Modeling demand distribution with selling constrained by stock

I'm working as a Data Scientist on a project where we are supposed to determine how many pieces of stock a certain retailer should have in each of its physical stores. The stock should be set on the ...
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### How do you test if the average of a population is the same as the variance of the same population?

What can be a statistical test to find out if a population has the mean equal to its own variance? I.e. Mean(X)=Var(X)? I am interested in it because Poisson regression makes the assumption that the ...
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### Suggestions for an independence test in a complex design

In an experiment I surveyed the effect of two treatments (pre & post) in different species. After every experimental run I tested whether the measured average effect was greater, smaller or not ...
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