# Tagged Questions

A discrete, univariate distribution modelling the number of ${\rm Bernoulli}(p)$ trial successes until a specified number of failures occur.

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### When to use zero-inflated poisson regression and negative binomial distribution

I have a fairly simple dataset looking at the relationship between the first nesting date of a bird in a given year (Date) and the birds overall fledgling production from that year (Fledge; count data ...
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### Interpretation of log transformed predictor in negative binomial regression

I mainly want to make sure that I'm making the correct interpretation here. I built a negative binomial regression model predicting a count variable. There was evidence of overdispersion or I would ...
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### Quantiles of a compound gamma/negative binomial distribution

Are there any formulae for the quantiles of a compound gamma/negative binomial distribution? That is, suppose we have $$N \sim \text{NegBin}(\alpha, \lambda)$$ and conditional on $N$, Y = ...
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### Interpretation of $\theta$ in negative binomial regression

First off, a very similar question has been asked before. But the answers to this question did not explain what high/low values of theta mean. Here's my crack at trying to figure out what high/low ...
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### Zero-inflated negative binomial model for true zeros

The zeroinfl function in the pscl package in R assumes that zeros include both false zeros and true zeros. I have a zero ...
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### Increased Type I error - GLM

Some of you might have read this nice paper: O’Hara RB, Kotze DJ (2010) Do not log-transform count data. Methods in Ecology and Evolution 1:118–122. klick. In my field of research (ecotoxicology) ...
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### Generate pseudo-random overdispersed Poisson numbers

I have multiple sets of data which conform to overdispersed Poisson distributions which I can model with the alternative parameterization of a negative binomial distribution ($\mu$ and $D$ instead of ...
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### GLM regression - help choosing model specification

I think I need to use a Poisson-family regression or negative binomial regression. My variables are as follows: Y is an integer value ranging from 0 to ~1200. It represents sums (number of species ...
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### Validating residual plot count data (different levels)

I am studying the distribution of a marine species using the number of sightings as a dependent variable. When I am trying to validate the plots of the best model I am getting a non-usual pattern, and ...
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### Use law of total variance to find unconditional variance of overdispersed Poisson?

First, I need to prove that the distribution of a RV X, where X|lambda ~ Pois(lambda), and lambda ~ gamma(a, B), is a negative binomial. I know that it is, but why negative binomial instead of another ...
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### Does and 95% CI containing 1 imply no difference in IRR calculations in the same was as in OR calculations?

My understanding is that with an odds ratio (OR) that a 95% CI containing 1 means that there is no difference between the odds of something occurring between groups. I wondered if this holds true for ...
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### Bootstrap of parameter estimates and confidence intervals (hurdle model)

Think you can help with this. I´ve run a set of candidate hurdle models on insect abundance data with pscl package for R. These models had an abundance part with a truncated negative binomial ...
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### How to evaluate goodness of fit for negative binomial regression

I'm trying to fit a model estimating waiting time using negative binomial regression, but I'm not sure how to assess the goodness of fit for my model. I would like to compare the negative binomial ...
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### correct use of Negative Binomial with a Geometric distribution in a mixed model (glmmPQL)

I am trying to fit a NB GLMM with a gemoetric distribution. I have come across very little information on this form of regression. And would like some pointers/reasurance. some literature is ...
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### does the equivalence of Poisson and conditional logit models hold for fixed effect panel data and negative binomial models?

Guimaraes et al. (Rev Econ Stat, 2003, 85/1) describe the conditions under which the results from poisson regression models and conditional logit models are equivalent. I am trying to find out whether ...
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### Basic idea of zero inflated two part models(hurdel) and application to big data (machine learning)

I'm currently working on the data which has 90% 0s in response variable. Based on my research, it seems zero inflated models could be a solution to this. However, while I was reading related ...
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### R² (squared) from a generalized linear mixed-effects models (GLMM) using a negative binomial distribution

I try to compute the marginal and conditional R² for a GLMM using a negative binomial distribution by following the procedure recommended by Nakagawa & Schielzeth (2013) . Unfortunately, the ...
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### Estimating abundance using non-normal count data

I have sample counts of $n=20$ or $n=7$ taken from right-skewed and zero-inflated populations. The challenge in each case is to use the sample to estimate the total count in that population. Each of ...
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### Limits of zero-inflated negative binomial in % of zeroes

What are the limits of a zero-inflated regression? Specifically, if more than 80% of the data is zeroes, is the ZINB still valid? What is a good rule of thumb or educated way to understand the right ...
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### Zero inflated negative binomial with selection

I am looking for a Stata (or R/Matlab if there's no Stata) implementation of the model described by Greene (1994) (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1293115). It is essentially a ...
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### comparing same negative binomial models built with subset data

I have a dataset made our of several stacked datasets (one for each state). I want to check whether a zero inflated negative binomial model with data from an individual state is different from the ...
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### GAM with negative binomial and temporal autocorrelation

I want to fit a GAM in R. My data are negative binomial. Plus they have a temporal autocorrelation. ...
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### Controlling for variables in negative binomial regression

I would like to run a negative binomial regression, but also controlling for one of the variables. Similar to what you would do with a hierarchical regression. I am trying to predict violence (never, ...
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### Leave-one-out cross-validation for negative binomial

I've just started working with the GLM negative binomial and I was wondering if it's possible to carry out a leave-one-out cross-validation for negative binomial GLM as I'm having troubles doing it ...
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### In a Poisson process measured with some efficiency, is the measured count still Poisson?

Situation: Say I have a Poisson process, like radioactive decay, producing R particles per second. I measure with a detector. There is a probability P that a particle will be detected by the ...
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### I got a good OLS fit for integer variables, do I still need to use count data methods?

First of all, I'm not a statistician, but I'm teaching myself some methods I require for a project I'm doing now. I have a 2D dataset of N observations. For the ith observation, the first entry is ...
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### Can i use a mixture model for when I have an omitted variable?

I plan to fit a GAM or GAMM. There is one categorical variable which I think is important for explaining Y (or Y*), but it is not in my dataset - it is measurable but has not been measured. Can I use ...
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### Why are Pearson's residuals from a negative binomial regression smaller than those from a poisson regression?

I have these data: set.seed(1) predictor <- rnorm(20) set.seed(1) counts <- c(sample(1:1000, 20)) df <- data.frame(counts, predictor) I ran a poisson ...
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### fisher information matrix of Negative Binomial distribution

can anyone show me how to find the Fisher information matrix for negative binomial distribution, if I parameterize the Negative Binomial distribution using parameters mean and size. Thank you!
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### Why do ANOVAs and GLM (negative binomial model) give different results for interaction effects?

In my study, children repeat sentences and I count the errors (DV = error rate). Children are divided into two groups (Group factor), and there are two different types of sentences (Condition factor). ...
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### Zero-inflation on steroids: choose among Poisson, negative binomial and zero-inflated regressions

I am struggling to fit alternative count models into my data. I guess my problem is just too many zeros. This is my data ...
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### Negative binomial distribution fit

I am trying to fit a negative binomial distribution, in R, to my over dispersed data (out of 20 ,14 samples are 0, and rest are less than 5). The mean is $-0.8$ and ...
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### Hyper-prior for negative binomial in hierarchical model using JAGS/BUGS

Below I'm using a negative binomial because it is more flexible than a simple poisson model. The data are counts $y$ of events for 16 individuals $x$. There are 14 counts (i.e. counting periods) for ...
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### Does the estimated overdispersion parameter of Negative Binomial depend on mean

Negative Binomial distribution can be parameterized using mean, $\mu$, and overdispersion $\psi$, so that the variance of NB is $\mu + \frac{\mu^2}{\psi}$. We know there is no analytical solution for ...
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### Evaluate deviation from negative binomial model

I'm trying to figure out how to determine to what extent a sample deviates from a negative binomial model fitted to a larger population. As an example, I generated counts of doctor visits for a ...
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### Standardizing count variables in panel data with overdispersion - R or Stata

I'm running a regression where the dependent (response) variable is a highly dispersed (slightly zero-inflated) count and the explanatory (independent or predictor) variables are continuous, counts as ...
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### Error in fitting negative binomial regression model in R when replicating published results (works in Stata)

I'm trying to replicate the results of the first model of this article: Hultman, Lisa, Jacob Kathman, and Megan Shannon. 2013. “United Nations Peacekeeping and Civilian Protection in Civil War.” ...
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### Interpreting ZINB - inflation model non-significant

I have a zero-inflated negative binomial model to a dataset (n = 47) with a over-dispersed dependent variable (...
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### Parametrization of Gamma and Negative Binomial in R

I have some Poisson data {${y_1,...,y_n}$} and a Gamma prior, and I wish to construct a predictive posterior distribution. As I understand, if my Gamma hyperparameters are $\alpha$ (the prior number ...
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### Analysis of rates and post hoc test with offset variable using glmer.nb

I am investigating variation in pollinator visitation rate (number of visits per inflorescence) with treatment and time category as fixed factors. Block is a random factor. Following Zuur et al. ...
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### Comparison between normal glm and glm.nb regression with quadratic term?

Let's say I have a function to simulate data for negative binomial regression: ...
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### Estimating Negative Binomial Regression Model

It is easy to estimate a Poisson regression model using the Newton–Raphson Iterative Technique as it only involves one parameter (mu). However, I am unable to understand how a negative binomial ...
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### Exp(B) value outside 95% Wald Confidence Interval

I ran a negative binomial regression on some count data using SPSS. The intercept had an Exp(B) value below the lower limit of the 95% Wald Confidence Interval. I've never seen this happen before ...
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### Negative binomial distribution mixture model with R

I have two data vectors of observed count data: $A$ and $B$, where count $A_n$ and $B_n$ refer to the same observation point. $A$ is assumed to follow a negative binomial distribution. $B$ is assumed ...
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### How can one test the assumptions of a zero-inflated negative binomial model in R?

I have fitted a zero-inflated model with a random effect using a negative binomial distribution in R, using the function glmmadmb. This is due to a large number of zeros and over dispersion. For a ...
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### extremely left-skewed response variable - how do I model this dataset?

This is a histogram showing my response variable. The response is # (or proportion? or percent?) of aphids eaten off of cards in fields, to model predation by natural enemies. Predictors: fixed ...