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31 votes
Accepted

Continuous generalization of the negative binomial distribution

That's an interesting question. My research group has been using the distribution you refer to for some years in our publicly available bioinformatics software. As far as I know, the distribution does ...
Gordon Smyth's user avatar
  • 13.2k
28 votes
Accepted

How to deal with overdispersion in Poisson regression: quasi-likelihood, negative binomial GLM, or subject-level random effect?

Poisson regression is just a GLM: People often speak of the parametric rationale for applying Poisson regression. In fact, Poisson regression is just a GLM. That means Poisson regression is justified ...
AdamO's user avatar
  • 63.7k
28 votes
Accepted

Expected number of times to roll a die until each side has appeared 3 times

Suppose all $d=6$ sides have equal chances. Let's generalize and find the expected number of rolls needed until side $1$ has appeared $n_1$ times, side $2$ has appeared $n_2$ times, ..., and side $d$ ...
whuber's user avatar
  • 329k
25 votes

What is the appropriate model for underdispersed count data?

The best --- and standard ways to handle underdispersed Poisson data is by using a generalized Poisson, or perhaps a hurdle model. Three parameter count models can also be used for underdispersed data;...
Joseph Hilbe's user avatar
21 votes

Interpretation of .L & .Q output from a negative binomial GLM with categorical data

Your variables aren't just coded as factors (to make them categorical), they are coded as ordered factors. Then, by default, R fits a series of polynomial functions to the levels of the variable. ...
gung - Reinstate Monica's user avatar
20 votes

Diagnostic plots for count regression

This is an old question, but I thought it would be useful to add that my DHARMa R package (available from CRAN, see here) now provides standardized residuals for GLMs and GLMMs, based on a simulation ...
Florian Hartig's user avatar
20 votes

Diagnostics for generalized linear (mixed) models (specifically residuals)

This is an old question, but I thought it would be useful to add that option 4 suggested by the OP is now available in the DHARMa R package (available from CRAN, see here). The package makes the ...
Florian Hartig's user avatar
19 votes
Accepted

How can I model flips until N successes?

The distribution of the number of tails before achieving $10$ heads is Negative Binomial with parameters $10$ and $1/2$. Let $f$ be the probability function and $G$ the survival function: for each $n\...
whuber's user avatar
  • 329k
19 votes

Continuous generalization of the negative binomial distribution

Look at this paper: Chandra, Nimai Kumar, and Dilip Roy. A continuous version of the negative binomial distribution. Statistica 72, no. 1 (2012): 81. It's defined in the paper as the survival ...
Aksakal's user avatar
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15 votes
Accepted

How to formulate the offset of a GLM

I don't know where you heard that a Poisson or negative binomial with an offset is preferable to a binomial model for a number of individuals surviving out of an initial number; I would normally ...
Ben Bolker's user avatar
  • 44.5k
15 votes

How can I model flips until N successes?

We can model the game like this: Player A flips a coin repeatedly, getting results $A_1, A_2, \dots$ until they get a total of 10 heads. Let the time index of the 10th heads be the random variable $X$...
Danica's user avatar
  • 25.2k
14 votes

Relationship between Poisson, binomial, negative binomial distributions and normal distribution

The binomial distribution is the distribution of the number of successes in a fixed (i.e. not random) number of independent trials with the same probability of success on each trial. It support is ...
Michael Hardy's user avatar
13 votes
Accepted

Should point estimates for a parameter always be exactly in the middle of their 95% CI or does it depend on the distribution?

TL DR No, they don't have to be at the midpoint. There are at least two ways to show this. We could run the example from R help, and then use functions to get things: ...
Peter Flom's user avatar
  • 125k
12 votes

Expected number of times to roll a die until each side has appeared 3 times

The original version of this question started life by asking: how many rolls are needed until each side has appeared 3 times Of course, that is a question that does not have an answer as @...
wolfies's user avatar
  • 7,823
12 votes
Accepted

Help interpreting count data GLMM using lme4 glmer and glmer.nb - Negative binomial versus Poisson

I believe there are some important problems to be addressed with your estimation. From what I gathered by examining your data, your units are not geographically grouped, i.e. census tracts within ...
prestevez's user avatar
  • 261
11 votes
Accepted

How to compute intraclass correlation (ICC) for THREE-level negative binomial hierarchical model?

I don't know if you still need the answer for this, but I'll try anyway. The ICC for a two level negative binomial model (Tseloni and Pease, 2003) can be easily calculated by: $$ \rho = \frac{\...
prestevez's user avatar
  • 261
11 votes
Accepted

Type I and Type II negative binomial distribution in zero inflated negative binomial (ZINB) model

The difference between these two model families is the relationship between mean and variance. nbinom1 (also called quasi-poisson) variance = µ * phi where µ is the mean and phi is the over-...
D A Wells's user avatar
  • 385
11 votes

Competing negative binomials

You are performing the equivalent of throwing a coin with a probability $p=1/6$ of heads until either $a=5$ heads or $b=20$ tails ("non-heads") have appeared. If you have thrown it $n$ times, the ...
whuber's user avatar
  • 329k
11 votes
Accepted

Prolonged negative binomial beyond Poisson?

The answer is yes: the prolongating distribution is the Binomial distribution. The trilogy: Binomial|Poisson|Negative Binomial can be regarded as one single two-parameter distribution for a non-...
Yves's user avatar
  • 5,676
10 votes

Negative-binomial GLM vs. log-transforming for count data: increased Type I error rate

The O'Hara and Kotze paper (Methods in Ecology and Evolution 1:118–122) is not a good starting point for discussion. My most serious concern is the claim in point 4 of the summary: We found that ...
John Maindonald's user avatar
10 votes
Accepted

GAMM with zero-inflated data

In addition to mgcv and its zero-inflated Poisson families (ziP() and ziplss()), you might also look at the brms package by Paul-...
Gavin Simpson's user avatar
10 votes

Difference between geometric distribution and negative binomial distribution

Negative binomial is a distribution of a number of successes $k$ before observing $r$ failures when observing independent Bernoulli trials with the probability of success $p$. It has probability mass ...
Tim's user avatar
  • 140k
10 votes
Accepted

Zero-inflated Gaussian for weights below zero recorded as 0?

I think the model is more appropriately a left-censored Gaussian, since the process you describe is about discarding information below some value (in this case, the location is known to be 0, which is ...
Sycorax's user avatar
  • 92.6k
9 votes
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Poisson Gamma Mixture = Negative Binomially Distributed?

There are various ways a negative binomial distribution can come about. One of them, as Robert Long comments, is as a Poisson distribution whose parameter is itself Gamma distributed. The Wikipedia ...
Stephan Kolassa's user avatar
9 votes
Accepted

Dealing with heteroskedasticity in negative binomial GLM

This answer (Negative Binomial Regression and Heteroskedasticity) on the same forum explains very nicely that models such as yours are predicated on a certain type of relationship between the (...
Isabella Ghement's user avatar
9 votes

Standard negative binomial regression when counts are mainly zeros?

I don't quite think that a distinction between "true" and "untrue" ("false"?) zeros is very helpful. Zero inflated distributions arise naturally if your data generating ...
Stephan Kolassa's user avatar
8 votes
Accepted

conditional on the total, what is the distribution of negative binomials

Sorry for the late answer, but this bugged me as well and I found the answer. The distribution is indeed Dirichlet-Multinomial and the individual neg. binomial distributions don't even need to be ...
Martin Modrák's user avatar
8 votes

Negative Binomial Regression and Heteroskedasticity

Heteroskedasticity is relevant with ordinary linear regression, where there is an assumption that variance is constant (do not depend on the mean), known as homoskedasticity. But with alternative ...
kjetil b halvorsen's user avatar
8 votes

How is a negative binomial regression model different from OLS with a logged outcome variable?

Assuming you've already identified the predictor(s) of interest/importance, the considerations for a model (in approximate order of importance) would be: a. do you want to model the conditional mean ...
Glen_b's user avatar
  • 286k
8 votes
Accepted

What is the probability that a best of seven series goes to the seventh game with negative binomial

Summary: the negative-binomial based approach in the question ignores that either team can win Game 7. After correcting for this the results agree. Assumption Not explicitly stated in the question, ...
Juho Kokkala's user avatar
  • 7,933

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