39
votes
Accepted
Negative binomial distribution vs binomial distribution
The difference is what we are interested in. Both distributions are built from independent Bernoulli trials with fixed probability of success, p.
With the Binomial distribution, the random variable X ...
- 931
31
votes
Accepted
Diagnostics for generalized linear (mixed) models (specifically residuals)
This answer is not based on my knowledge but rather quotes what Bolker et al. (2009) wrote in an influential paper in the journal Trends in Ecology and Evolution. Since the article is not open access (...
- 5,556
30
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 ...
- 12.1k
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 $d$ ...
- 316k
26
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 ...
- 60.4k
23
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;...
- 231
22
votes
Negative binomial distribution vs binomial distribution
Negative binomial distribution, despite seemingly obvious relation to binomial, is actually better compared against the Poisson distribution. All three are discrete, btw.
In practical applications, ...
- 60k
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. ...
19
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 ...
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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\...
- 316k
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 ...
- 60k
17
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 ...
- 7,719
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 ...
- 41.4k
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 $X$...
- 24.2k
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 ...
- 8,796
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:
...
- 109k
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 @...
- 7,583
11
votes
Accepted
An impossible estimation problem?
Basically, for your sample, the estimate of the size parameter is on the boundary of the parameter space. One could also consider a reparameterization such as d = size / (size+1); when size=0, d=0, ...
- 126
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-...
- 385
11
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 ...
- 241
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 ...
- 316k
10
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{\...
- 241
10
votes
Negative binomial distribution vs binomial distribution
They are both discrete and represent counts when you are sampling.
Binomial distribution represents the number of successes in an experiment which its number of draws is fixed in advance ,for example ...
- 1,583
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-...
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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 ...
- 88.9k
9
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 ...
- 461
9
votes
Accepted
Fitting negative binomial distribution to large count data
Firstly, goodness of fitness tests or tests for particular distributions will typically reject the null hypothesis given a sufficiently large sample size, because we are hardly ever in the situation, ...
- 30.4k
9
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♦
- 135k
9
votes
Accepted
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 ...
- 117k
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 ...
- 2,473
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