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Questions tagged [negative-binomial-distribution]

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

Overview

The negative binomial is a discrete, univariate distribution modelling the number of ${\rm Bernoulli}(p)$ trials until a specified number of failures occur. It is parametrized by $r$, the number of failures in $k$ ${\rm Bernoulli}(p)$ trial successes.

A discrete random variable $X$ has a negative binomial distribution, indexed by parameters $p \in (0,1)$ and $r \in \mathbb{Z}$ if its probability mass function is

$$ \Pr(X = k) = {k+r-1 \choose k} (1-p)^r p^k $$

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Diagnostic plots for count regression

What diagnostic plots (and perhaps formal tests) do you find most informative for regressions where the outcome is a count variable? I'm especially interested in Poisson and negative binomial models, as well as zero-inflated and hurdle counterparts…
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Understanding the parameters inside the Negative Binomial Distribution

I was trying to fit my data into various models and figured out that the fitdistr function from library MASS of R gives me Negative Binomial as the best-fit. Now from the wiki page, the definition is given as: NegBin(r,p) distribution describes the…
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When do Poisson and negative binomial regressions fit the same coefficients?

I’ve noticed that in R, Poisson and negative binomial (NB) regressions always seem to fit the same coefficients for categorical, but not continuous, predictors. For example, here's a regression with a categorical…
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What are the assumptions of negative binomial regression?

I'm working with a large data set (confidential, so I can't share too much), and came to the conclusion a negative binomial regression would be necessary. I've never done a glm regression before, and I can't find any clear information about what the…
Carly
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Difference between binomial, negative binomial and Poisson regression

I am looking for some information about the difference between binomial, negative binomial and Poisson regression and for which situations are these regression best fitted. Are there any tests I can perform in SPSS that can tell me which of these…
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Negative binomial regression question - is it a poor model?

I am reading a very interesting article by Sellers and Shmueli on regression models for count data. Near the beginning (p. 944) they cite McCullaugh and Nelder (1989) saying that negative binomial regression is unpopular and has a problematic…
Peter Flom
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What is theta in a negative binomial regression fitted with R?

I've got a question concerning a negative binomial regression: Suppose that you have the following commands: require(MASS) attach(cars) mod.NB<-glm.nb(dist~speed) summary(mod.NB) detach(cars) (Note that cars is a dataset which is available in R,…
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Diagnostics for generalized linear (mixed) models (specifically residuals)

I am currently struggling with finding the right model for difficult count data (dependent variable). I have tried various different models (mixed effects models are necessary for my kind of data) such as lmer and lme4 (with a log transform) as well…
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Negative binomial distribution vs binomial distribution

What is the difference between the negative binomial distribution and the binomial distribution? I tried reading online, and I found that the negative binomial distribution is used when data points are discrete, but I think even the binomial…
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Where does the offset go in Poisson/negative binomial regression?

(First of all, just to confirm, an offset variable functions basically the same way in Poisson and negative binomial regression, right?) Reading about the use of an offset variable, it seems to me that most sources recommend including that variable…
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Continuous generalization of the negative binomial distribution

Negative binomial (NB) distribution is defined on non-negative integers and has probability mass function$$f(k;r,p)={\binom {k+r-1}{k}}p^{k}(1-p)^{r}.$$ Does it make sense to consider a continuous distribution on non-negative reals defined by the…
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What is the appropriate model for underdispersed count data?

I am trying to model count data in R that is apparently underdispersed (Dispersion Parameter ~ .40). This is probably why a glm with family = poisson or a negative binomial (glm.nb) model are not significant. When I look at the descriptives of my…
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Why is a "negative binomial" random variable called that?

I don't understand why the "negative binomial" random variable has that name. What is negative about it? What is binomial about it? What is negative-binomial about it?
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Switch from Modelling a Process using a Poisson Distribution to use a Negative Binomial Distribution?

$\newcommand{\P}{\mathbb{P}}$We have a random process that may-or-may-not occur multiple times in a set period of time $T$. We have a data feed from a pre-existing model of this process, that provides the probability of a number of events occurring…
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Why is the quasi-Poisson in GLM not treated as a special case of negative binomial?

I'm trying to fit generalized linear models to some sets of count data that might or might not be overdispersed. The two canonical distributions that apply here are the Poisson and Negative Binomial (Negbin), with E.V. $\mu$ and variance $Var_P =…
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