# Questions tagged [overdispersion]

Overdispersion is when there is greater variability than there 'ought' to be in the data. Eg, the variance of counts is often greater than the mean, whereas the variance of a Poisson should equal the mean.

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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-...
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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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### How does one deal with linear regression with heteroscedasticity?

Suppose I have a dataset with outcome continuous. I applied various transformations on either covariate, outcome or both. I have also tried polynomial terms. I always get over heteroscedasticity when ...
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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 ...
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### Interpretation of Dispersion Parameter and Intercept in ZINB Model

I am doing my first own data analysis and I'm new to more complicated mixed models. I fitted a ZINB model with the glmmTMB package with the following code: ...
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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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### Dispersion parameter in negative binomial

I simulate data from a Gamma-Poisson model in R as follows. The mean and variance of the negative binomial distributed counts are $a b=10$ and $a b (1+b)=60$. ...
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### Does changing model due to overdispersion/underdispersion results in forking?

This is related to the post How much do we know about p-hacking "in the wild"?. The post does not clearly delineate the boundary between forking or not forking to me. Suppose I have a count ...
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### What is an alternative to Chi-Square for observed vs. expected variance suitable for repeated measures?

I want to test for individual-level side preference of a behaviour during an experiment, and found a way to do this using a chi-square test that uses the number of right (or left) turns out of the ten ...
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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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### How to fit overdispersed count data in R using INLA package?I have tried the Neg Binomial family already! I would like to use other family in R?

I would like to know how to fit a spatial conditional Poisson and Neg Binomial in R using INLA to cater for overdispersed counts data.
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### What better I use for Negative Binomial Regression with library(MASS) glm(family=negative.binomial) or glm.nb?

Hay, im a newbie and still need more learn. I have several question, I'm trying to create a negative binomial regression model using the R and library(MASS). But i'm still confusing what sould I use ...
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### Is overdispersion possible in binomial logistic regression model that is not subsettable?

I’m creating a binomial logistic regression model with two variables: average tree height within a survey site and tree density within that same site. For each site, I only have one measurement for ...
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### How to develop a negative binomial model where the overdispersion parameter varies as a function of one of the independent variables/covariates?

I am trying to develop a negative binomial model where the dependent variable is crash count, and the independent variables are traffic count and roadway length. Currently, with the below code, I get ...
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### Are overdispersion and underdispersion in a binomial logistic regression model an issue if the model is not being used to make predictions?

If a binomial logistic regression model is being used strictly to identify variables that have an impact on the dependent variable but is not being used to make predictions, are underdispersion and ...
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### Should observation level random effects be included when modeling dispersed counts in a negative binomial model?

I am trying to specify a model of counts from very different observation sites. Including site level random effects would definitely make sense since there are aspects that are certainly not covered ...
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### Cross validation and aggregated data for count models

I know that this question has already been formulated in other posts where there are quite comprehensive answers, I refer especially to these two explanations (thread1, thread2). However I continue to ...
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### When does a group specific dispersion parameter for the negative binomial distribution make sense?

If you have overdispersed observed abundance of multiple species including zero inflation the negative binomial distribution seems to be a reasonable choice. But if some species occur much more ...
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### Residuals of GAM models not improving with poisson or ziplss, but better with negative binomial (help with high values)

I am running GAM models on species counts with lots of zeros and high values or high counts. Residuals under poisson family have a s-like curve on qq line with models not predicting lower and higher ...
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### Meaning of "Overdispersion" in Statistics

I am trying to understand what "overdispersion" means in statistics. Based on the Wikipedia page, "overdispersion" is defined as follows : "In statistics, overdispersion is ...
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### Overdispersion strategies for exponential curve fitting GLM?

I have price-volume (demand curve) data that follows the exponential function. I used a Bayesian model via PyMC3 to visualize the posterior distribution. This model is simply linear regression in log ...
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### Is there any R packages allow direct MLE estimation of dispersion in negative binomial distribution?

Using the built-in function, I can get ...
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### What does the dispersion parameter means in negative binomial regression?

I am completely new to the topic of negative binomial regression and am unsure about what the output of my regression exactly means. Before I decided to use the negative binomial regression, i did ...
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### Why fitting a Poisson GLM in an over dispersed dataset underestimate the standard error of the regression parameter?

It is claimed by many authors that if we fit the GLM Poisson model to an over dispersed dataset of count data, the standard error of the estimated coefficients will be under-estimated. Could you ...
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### Dealing with singularity and overdispersion in GLMM?

I'm running a GLMM through the lme4 package in R to detect differences in time spent feeding (response) before and after birth (my 2 categories in the variable inf_cat). I started with a poisson GLMM, ...
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### How do I deal with ties when using rank-based normalizing transforms, e.g. Blom?

I would like to transform heavily skewed data with range (-Inf, Inf) and heavily zero-inflated into a form suitable for using GLMs for significance testing. Zero-inflation precludes the effective use ...
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### For overdispered data, should the correlation matrix exclude zero?

I have 4 species and their distributions are overdispersed in space (i.e. lots of zeros). I calculated a Pearson correlation matrix and there is a lot of cluster around the 0s and 1s. Should I ...
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### Modelling overdispersed rate data using a negative-binomial distribution

A quick overview of the analysis I'm wanting to do: I am wanting to analyze the relationship between habitat factors and the capture of my research species over a network of traps, in order to be able ...
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### How to correct pattern in residuals when using a negative binomial distribution? Is it due to overdispersion?

I have a large dataset with the count data and I computed the following full model (covariates are all scaled) : ...
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### How to work with continuous overdispered data?

I have troubles with analysis of my data. I analyze cross-sectional data about users activities and spendings from mobile game . I have paying and non-paying users, I need to explain what independent ...
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### How to correct conditional Poisson standard errors for over-dispersion

I want to estimate a conditional negative binomial model, which an economist might call a negative binomial model with individual fixed effects. I use Python and statsmodels, which has a conditional ...
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### Python statsmodels, handling over-dispersion for Poisson Regression

I have a Poisson model (displayed below), where my $\epsilon_e$ term is designed to handle over-dispersion. I was curious if statsmodels has an easy way of returning a coefficient $\epsilon$ that fits ...
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### Conf intervals on the dispersion coefficient of quasibinomial GLM or binomial GLMM with obs-level random effect

In this post I see how they calculate the confidence interval on the theta parameter of a negative binomial GLM: Confidence Interval for the Dispersion parameter of negbin distribution. I typically ...
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### What is the difference between conditional and unconditional fixed effects?

What is the difference between unconditional and conditional (fixed effects negative binomial) regression models? A similar question was asked for quantile regression here: What is the difference ...
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### How to statistically test if the dispersion parameter in a negative binomial distribution is different?

I have a negative binomial distribution for two species. I have been able to fit (dummy) data to estimate mean (mu) and dispersion parameter (size). However, I want to statistically test if the two ...
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### How can I resolve overdispersion in a negative binomial model?

I started what seemed like a straightforward analysis, but I've gotten stuck with overdispersion in my negative binomial model. I would like to know which sites are different from each other in terms ...
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### Overdispersion in logistic model

I'm relatively a newbie in R, and I've been trying to make a silly example of logistic regression to predict, according to Age and Sex whether someone dies of corona or not. I'm from Colombia, so my ...
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### How different from one does a dispersion ratio have to be to be considered significant?

I am in the process of conducting zero-inflated generalised mixed effects models with Poisson distributions and have been using the testDispersion() function of the DHARMa package in R to determine if ...
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### Error in a zero-inflated negative binomial model?

Following DHARMa diagnostic tests revealing zero-inflation (ratioObsSim = 32.663, p < 2.2e-16) and over-dispersion ...
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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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### What is the best way to deal with over-dispersion in a poisson GLMM?

I am currently in the process of trying to complete a poisson GLMM analysis with two fixed (with an interaction) and two random effects using the glmer() function of the lme4 package. Using the ...
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### Sum of non-identical Bernoulli is overdispersed or underdispersed Binomial?

Extra-binomial variation is defined in this Oxford Reference source: Greater variability in repeat estimates of a population proportion than would be expected if the population had a binomial ...
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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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### How to perform negative binomial regression on gut microbiome data with over dispersion?

Thank you guys so much in advance! I got a table, containing the information of gut microbial composition of different groups, that is, the count data of different bacteria in each sample of different ...
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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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### Trade-off between explaining variance and correcting overdispersion

I am fitting linear model. I happen to be working in R, and the specific model I'm fitting is a generalized additive model using the package mgcv, but I think all that is incidental to my question. ...
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### GLMER Overdispersion and Error messages

I have a data set which involves 30 binomial absence/presences totalled for a ratio out of 1, which is the total score of a test out of 30 marks. The data requires fitting one of my predictor ...
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### Can we mix conclusions from Poisson and Quasi-Poisson?

Currently I'm working with ecological studies, where my response is a count variable. I need to estimate several models, each one represents a city. Afterwards I aggregate them to obtain meta-analysis ...
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Suppose we have some count data, and we want to use a model that allows for "overdispersion" or "underdispersion" in the data (i.e., higher or lower variance than the Poisson distribution). Let $X$ ...