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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13 views

Trying to choose between a LM or a GLM (family=negative binomial)?

I have data on captures per year (n=13) and I want to analyze the relation with years (is it increasing, decreasing or staying the same with time). Total captures ~ year Because is number of ...
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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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26 views

How to choose the appropiate beta regression model type and variables?

Recently, I got my hands on modelling proportions [0,1]. Due to data type many of my variables are 0 and 1 inflated. Some of them are delicately affected by the bound values and some are heavily. I ...
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31 views

Interpretation of zeroinfl vs. glm.nb results

I am trying to test effects of 3 predictors on overdispersed count data with many zeros, and a Vuong test suggested that a zero-inflated neg. binomial model would fit better than a negative binomial ...
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Appropriate model for count data when response variable minimum value is far above zero

CASE 1: I am trying to model count data; the response variable, y=c(12, 15, 34, 13, 12, 33,....,45) while the explanatory variables are location (binary, rural/urban), marital status, education level, ...
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174 views

Overdispersion in fitted generalized linear model with insignificant regression coefficients

Overdispersion is the phenomenon of having data that is more variable than its model assumes. Overdispersion can occur when the model in question has inseparable mean and variance parameters. If I ...
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45 views

Confused about over dispersion for my beta distribution

I have percentage data so I am using a beta distribution and I want to do a mixed-effect model so I am still trying to decide between glmmTMD or the brm packages. I saw somewhere that some ...
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How to analyze data for spatial aggregation and niche overlap with no specific GPS points over time?

I study soil insects, and sample monthly for insects. Each month, I sample at 8 different sites. Each site is divided roughly into 4 meter square quadrants (shown in figure). From each quadrant, I ...
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Looking for a discrete distribution with a specific mean-variance relationship

Say we have some counts $Y$ for which the mean-variance relationship is $$ Var[Y] = \alpha E[Y] + \beta E[Y]^2. $$ From this, we can say that: If $\alpha = 1$ and $\beta = 0$, then $Y$ can be ...
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How to use quasi-Poisson model after overdisperson with glmer(mydata,family = poisson(link = 'log'))?

I have to fit my data with Laplace glmm with random effect using poisson distribution error. ...
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23 views

beta binomial to reduce overdispersion for binomial data (zero inflation)

I know that a negative binomial model is often use to solve the problem of overdispersion in count data (poisson regression). Now, someone said that a beta binomial model can also be used to solve the ...
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49 views

What actually happens when we model a frequency instead of count (POISSON GLM)

First of all, I am using R. I know that we can model a frequency-response variable with a poisson regression, if we remember to weight it, so that the variance doesn't get affected by it. I am not ...
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172 views

Is an overdispersion parameter of 5.17 for GLMM with Beta family too high to yield reliable results?

I'm running a generalised linear mixed model with beta family on the effect of overhead cover (proportion ∈ (0,1)) on the proportion of birds scavenging from carrion left out in nature (proportion ∈ (...
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How to prove overdispersion in Poisson regression?

For $Y_i$ independent $ \sim \mathcal{Poisson}(λ_i)$, $i = 1, \dotsc,n$, I want to assume $λ_i$ has mean $λ$ and variance $σ^2$. With this I want to show the following, but I am not sure how to show ...
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104 views

Determining overdispersion of count variable in bayesian model (brms)

I am trying to determine whether my response count data are too overdispersed for a (brms) Bayesian poisson model. I constructed a poisson-generated response variable with low and high levels of noise/...
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Does one need to run a poisson regression to estimate the scale parameter before using negative binomial regression?

The negative binomial has two parameter in its distribution. Neg bin has a scale and a probability parameter. I’d imagine the scale parameter estimated in poisson regression is only one of them. Does ...
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Does poisson GEE require “scale.fix=TRUE” and “scale.value=1”?

Does poisson gee require scale.fix=TRUE and scale.value=1 for the package geepack? Aside: I heard gee package in r doesn't allow one to specify the scale.value and only let's one specify scale.fix=T/...
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Why ever use a quasipoisson model instead of bootstrapped poisson GLM?

A poisson GLM and a quasipoisson regression model will given identical point estimates for the beta parameter of the linear predictor. The quasipoisson model is typically used when there is ...
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Hypothesis Testing with Chi-Squared: Is Overdispersion a concern?

Assume an AB test design, with one experimental group, one control group, and an anticipated effect on a conversion rate. The chi-squared test only takes as input successes/trials for each group. ...
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Test for overdispersion glm negative negative binomial in stata

I have a time series of count data. I need to use Newey-West SEs and therefore need to use the glmcommand with ...
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Wald test for Overdispersion in Poisson Regression model [duplicate]

could you kindly help me with the test statistics for performing an overdispersion test in R for Poisson and negative binomial regression models?
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38 views

Fish counts and Poisson [closed]

I am having troubles with fitting a Poisson distribution to my data, let me explain: I have fish counts of different species from a closed list, at 5 sites, 2 different depths, and across 10 years. ...
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106 views

Overdispersion vs Tweedie

I am dealing with data that could possibly be overdispersed and I am looking at fitting a GLM with a quasi distribution. As far as I understand, when we fit a glm ...
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Overcoming model singularity in overdispersed data set

I am analysing a data set that is created from walking transects and recording counts for each group size of animals observed. Each transect has 41 repeats, which was approximately 80% zeros. However, ...
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300 views

Help interpreting output from glmmTMB and Ben Bolker's overdispersion function

Just wondering if anyone can help with interpreting the output from Ben Bolker's over-dispersion function (please see link below): https://bbolker.github.io/mixedmodels-misc/glmmFAQ.htmlhttps://...
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Probability of multiple parasites given the presence of one parasite

I am trying to simulate parasitic plants that infect trees. I would like to test wether the presence of one parasite makes it more likely that the tree has more than one parasite. The number of trees ...
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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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264 views

DHARMA to detect overdispersion in negative binomial

I'm new to negative binomial GLMMs and still trying to get a hold of checking my residuals. DHARMa has been a huge help, but I still am having some inconsistent results. I am looking at three groups ...
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422 views

Dealing with Overdispersed Negative Binomial using glmmTMB

I'm new to the world of statistical modeling, but I was wondering if anyone had any input on how to handle overdispersed negative binomial data? I'm working on modeling bat activity as a response ...
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103 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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1answer
65 views

`dispersiontest()` estimates dispersion too small

I am using dispersiontest(fit, trafo=2) from the AER package in R to see if my data is overdispersed and what the dispersion parameter $\alpha$ is. Since I use <...
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37 views

GAM model residuals

I have a huge problem with my model. I did a GAM Model with negative binomial distribution (with mgcv library). Now I want to do an overdispersion test but I think that this doesn't exist for ...
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Is my overdispersion too large in this quasibinomial model?

I have used a quasibinomial model on my data, but my overdispersion coefficient seems to be too large with a value of 40.78776. ...
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204 views

How do I carry out a significance test with Tarone's Z-statistic?

Context In this blog the author suggests using Tarone's Z-statistic to test for overdispersion in a binomial model to determine whether or not it is necessary to use a beta-binomial model instead. In ...
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233 views

Overdispersion tests from DHARMa and sjstats: conflicting results?

I ran some models for my count data, and did some diagnostics to check for overdispersion. Here is a dharma graph, which as I understand, indicates no overdispersion. And this is the result I get ...
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129 views

Adjusting for clustering and overdispersion in count models

My question is specific to the estimation of glm's and correcting for 'clustering' in a quasi-experiment (difference-in-differences). My outcome is counts of crimes....
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360 views

DHARMa diagnostics: testDispersion and testZeroInflation interpretation

I have been analyzing count data using Poisson distribution in glmmTMB, and just ran some DHARMA diagnostics. However, there don't seem to be a lot of help online on how to interpret the results. Does ...
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121 views

QQ plot doesn't look great - maybe quasipoisson with random effects?

I have several glmer()-models that look like this: ...
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31 views

Is there a way to address overdispersion in a gls model?

I have autocorrelated data that show a positive linear increase. When I model them using gls, I think the summary shows overdispersion. When using GLMM etc I'd change error structure, but I don't ...
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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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124 views

Poisson model appears overdispersed, but usual recommended approaches don't improve fit

Summary: I am trying to model some count data. I initially attempted to fit a poisson GLM, but diagnostics appear to indicate overdispersion. I have tried several different recommended remedies but ...
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95 views

MLE for Overdispersed Poisson

I searched for a while on Google and this website for an answer to this question. I have an overdispersed Poisson distribution and a "hand-wavy" proof is giving me problems. Below is the information ...
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940 views

Choosing the optimal theta / dispersion parameter for negative binomial regression (glm / glm.nb) in R

I am applying a negative binomial regression to my data in R. For this, I use the package MASS and have two different ways to calculate it: ...
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928 views

Are over-dispersion tests in GLMs actually *useful*?

The phenomenon of 'over-dispersion' in a GLM arises whenever we use a model that restricts the variance of the response variable, and the data exhibits greater variance than the model restriction ...
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635 views

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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1answer
246 views

How to perform over-dispersion test where null is quasi-Poisson

If I understand correctly, a quasi Poisson regression assumes roughly that $$ \mbox{E}\left[y\left|x\right.\right] = \exp{\left(x^{\top}\beta\right)}, \quad \mbox{VAR}\left(y\left|x\right.\right) = \...
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156 views

Overdispersion problem in a quasi-binomial GLM (for proportional data)

Below is the summary of a GLM I built for a response variable which is proportional (derived from count data). My only predictor is a continuous one (environmental measurement). And my sample size is ...
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65 views

Control for over-dispersion. Why do this: take natural log of metric, exponentiate, rank, remove top and bottom 10%

I'm looking at some NHS healthcare data on the number of deaths in England The measure i'm looking at is called the SHMI - it's simply: The number of observed deaths at a hospital / The expected ...
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1k views

XGBoost Poisson Objective Function When Data is Over-dispersed [closed]

I am modeling very over-dispersed count data with the goal of prediction. The data is not zero inflated (there are no zeros), but there are a lot of values of 1. ...
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84 views

Interpreting Quasi-Linear Regression Predictions

I know that for a simple linear regression the predictions are distributed like: $$y_i\, |\, x_i\, \sim\, \mathcal{N}\big(\widehat{\beta}_0+\widehat{\beta}_1\, x_i,\ \sigma^2\big)$$ $$\text{where: } \...