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# Questions tagged [underdispersion]

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

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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 deal with under-dispersion in negative binomial GLMM?

I have some animal species. I am interested in seeing what is the relationship between the area they occupy (my response variable, p, which is a count of cells) and ...
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### From overdispersion to underdispersion: comparing linear regression models with DHARMa

I have been investigating the relationship between the occurence of certain weather phenomena and time. To aid me in evaluating the fit of my (simple linear-regression) models, I have been using the ...
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### Why would a model indicate overdispersion without random effects but underdispersion with random effects? (and how to handle)

Overview: In my model building process, I fit both GLMs and GLMMs. I noticed that the GLMs suggested overdispersion in the data, while the GLMMs suggested underdispersion. How can I make sense of this,...
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### Dispersion parameter in DHARMA

I have a question about the interpretation of residual diagnostics using DHARMa. I fitted a binomial mixed model and used DHARMa for model diagnostics. ...
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### Count process with standard deviation proportional to its mean

What is (is there) the count process, which has its standard deviation proportional to its mean? Note that I am not talking here about Poisson process, which has its variance proportional to mean. ...
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### How to correct underdispersion in logistic regression

I created a logistic regression model with four continuous variables and a binary outcome. I divided the residual deviance by the residual degrees of freedom, which equaled 0.63. From my understanding,...
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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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### Explanation and simulation of under-dispersion in quasi poisson GLM

I'm currently working on analysis of excess mortality during the pandemic as part of my Master's thesis. I am using UK data, from Public Health England, who use a Quasi Poisson model for expected ...
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### Is underdispersion problemetic for predictive poisson models?

I am modelling some count data and I suspect my data to be underdispersed. I intend to use the Poisson distribution so that I can use information criteria (BIC) for optimal variable selection. However,...
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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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### Interpreting over/underdispersion of data with Poisson GLM in R

I have count data that I have fit a GLM to using the Poisson distribution and the default log link function. I have run a couple tests for over/under dispersion: Dividing the residual deviance by its ...
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### GLM for comparing multiple series of values

First I want to say that I'm a beginner at statistics so sorry if my question contains errors. I have analysed zebra finch song to find the time between the onset of notes in their song. For each bird ...
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### Checking Conway-Maxwell-Poisson model adequacy

I am trying to troubleshoot model adequacy problems for underdispersed count data (number of correct responses in a simple task; dispersion ratio is 0.3) that I modeled with Conway-Maxwell-Poisson. ...
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### Improving fit of underdispered beta regression model in glmmtmb

I have survey data where the outcome is the proportion of a research budget interviewees wished to assign to one of three different "types" of research into solutions for various issues. I ...
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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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### 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 poison regression model with ...
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### Zero-inflated generalized Poisson mixed effect model with glmmTMB still zero inflated

I am trying to analyze a dataset using number of flowers as response variable and the interaction between two treatment variables (categorical with 2 and 3 levels) as covariates. I also have a random ...
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### Modelling count data with extreme underdispersion - what distribution?

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 $X$ ...
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### Issues with Conway Maxwell Poisson Family in glmmTMB

I'm having issues running the the Conway Maxwell Poisson family (compois) in glmmTMB. I have under dispersed data (0.5). I am running a mixed model. 3 predictor variables, 2 random effects, n=1000. ...
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### GLMM - how unbalanced is unbalanced, how under-dispersed is under-dispersed?

I have a large data set, with vegetation data sampled at plots that are Sand or Clay soil type at 20 sites. I plan to fit a GLMM to the data, with 'soil type' as both a fixed effect and as a random ...
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### Is there a single discrete distribution that handles over and under dispersion? [duplicate]

I have some count data I am trying to model. The variance is very close to the mean, so the Poisson distribution for the entire data set seems like a good starting point. I have done and it seems to ...
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### Residual Deviance and degrees of freedom - Negative Binomial Distribution

I am trying to model count data using python's statsmodels module (Beer's sold at a football stadium as function of visitors, "tilskuer", and weather data). ...
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### fitting COM-Poisson in R

I have some crash data I did Poisson for that and the data was underdispersed. I want to do COM-Poisson regression for my data. I see that every website suggest several packages for COM-Poisson and I'...
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### Is there a common underdispersed discrete distribution with unbounded support for general mean and variance?

I have a mean $\mu$ and a variance $\sigma^2$ with underdispersion, i.e., $\sigma^2<\mu$. Is there a standard discrete distribution with these moments and unbounded-on-the-right support, i.e., ...
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### Interpreting dispersion for Inverse Gaussian GAM (log linked)

After reading Wood (2006), Zuur et al. (2009) and all questions related to GAMs here, I still haven't found the following: Should I calculate the dispersion for an ...
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### Name of the test for over/under dispersion

When testing for over or underdispersion in a count variable there is a test (available for example in the glm.nb() function in the ...
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### Is my variance compatible with a Poisson distribution

I have data coming from a genomics experiment which consists of 100s of thousands of observations (RNA sequencing reads) from 18 different indeviduals. Some of the samples come from one tissue some ...
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### Dealing with "underdispersion" in binomial GLMM

I try to fit several binomial glmms. My interest is wheather historic and recent samples differ in their climatic conditions. My data is organized as follows, where ...
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### Causes for Underdispersion in Poisson Regression

I am working with count data (number of pregnancies per woman), and using glm Poisson (log-link) to model determinants of the former count variable. From simple descriptives I observe that my data ...
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### Quasi-poisson for underdispersed data

Related to glm() in R, I saw a few post recommending modeling underdispersed data using the Conway–Maxwell–Poisson distribution, specifically with the R package <...
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### What distribution for Golf strokes?

I'm trying to find a distribution that adequately represents the number of strokes professional golfers make on a par 3 hole, so that I can simulate outcomes from this distribution. I have been ...
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### How to address underdispersion in a GLMM

I've read a few entries about underdispersion in count or binomial data, relating to poisson and binomial probability distributions. However, I haven't been able to find any information about gaussian ...
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### Sampling from under/over-dispersed count data in R

I am currently working a some datasets with count data in R, in which the response is the number of activities of a given type that were performed in one day by a population. For each type, I build ...
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### How to define the nu parameter of Conway-Maxwell-Poisson in spaMM package

I am trying to model some count data (clutch size) which are underdispersed. I want to account for different fixed and random (intercept) effects. My initial model was by using a random effect Poisson ...
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### Index of Dispersion - How to test its significance?

Starting from Poisson distribution and cluster analysis I am trying to find a statistical/empirical method in order to test if my Index of Dispersion (https://en.wikipedia.org/wiki/...
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### negative binomial for underdispersed data?

I've read in several places that a negative-binomial model is a reasonable alternative to a Poisson regression when the latter shows overdispersion. However, none of the several sources I read said ...
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### Forecasting a distribution for count data

I'm working on a project to forecast the distribution of a baseball player's "At Bats per game" (a baseball statistic w/ integer domain) using a player's position in his team's batting order as a ...
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### underdispersion in a binomial GLMM

I am trying to analyze data from an experiment in which I measured the learning of a colour preference in birds under two treatments. 40 Individuals were organized into 8 groups, and 4 groups were ...
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### Can I ignore under-dispersion in my count data?

I have under-dispersed count data. I do not want to transform them, and using a negative binomial error distribution (via glmer.nb) does not help. My results are ...
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### Modeling count data with underdispersion

I modeled the count data with Poisson regression and the Pearson chi square divided by the degrees of freedom was 0.25 suggesting under-dispersion , what can I do , is it possible to deal with this ...
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### How to do an ANOVA when your data are non-normal with possibly differing variances?

I wish to run an ANOVA on 13 groups: each group has a different sample size. Also, my groups are not normal and it barely passed Levene's test at $p=.052$. I have tried transformations by square ...
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### Does binomial distribution have the smallest possible variance among all "reasonable" distributions that can model binary elections?

Imagine an election where $n$ people make a binary choice: they vote for A or against it. The outcome is that $m$ people vote for A, and so A's result is $p=m/n$. If I want to model these elections, ...
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### How can I model such count data with underdispersion?

Here is an example of my data: 2 6 4 5 2 5 4 4 2 3 3 5 5 6 5 6 **15 19 16 9 14 14 11 10** 6 4 2 In my assumption, the sequence can be separated into regimes, for ...
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### GLM for proportional data and underdispersion

I'd like asking your help to understand a statistical issue from my data set. I ran a GLM with proportional data, using a binomial distribution. However, I've found underdispersion in my model and I ...
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### Overdispersion and Underdispersion in Negative Binomial/Poisson Regression

I was performing a Poisson regression in SAS and found that the Pearson chi-squared value divided by the degrees of freedom was around 5, indicating significant overdispersion. So, I fit a negative ...
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### Poisson regression with underdispersed and truncuated/censored upper bound

I'm analysing data from an experiment in which participants, over a number of trials, were presented with 8 boxes - 7 containing gold coins, and 1 containing a pirate. Their task was to open as many ...
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### Are these data underdispersed? If so, what mechanisms may explain this?

Say someone who is well practiced (appears to have reached a performance plateau) shoots 20 free throws on 15 different days and is successful the number of times shown in the upper histogram (...
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### How to deal with underdispersion with binomial data

I'm working with a pretty large dataset (n = 4,500) where 10% of my points (pixels in a GIS landscape) are 1s and the rest are 0s. The full model for my data looks something like this: ...
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### How to interpret underrepresented low p-values in Multiple Testing?

This is, I hope, quite a simple question. Being new to the concepts and methods of Multiple Testing, I've been histogramming some of the p-values I've been computing in my genomics research. What I ...
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