# Questions tagged [negative-binomial]

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

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15 views

### Correct expression of the coefficient for negative binomial distribution

I came across 2 sightly different expressions of the coefficient for negative binomial distribution: From Wikipedia, it expressed it as in $(k + r - 1)$ trials where $r$ denotes number of failures, ...
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### negative binomial inter-arrival

I am trying to find out what is the distribution governing the inter-arrival of events for a counting process that follows a negative binomial? I know for a Poisson counting process the inter-arrival ...
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### How to Calculate Sample Size Requirements for Quasi-Poisson / Negative Binomial AB Test in R

I'm doing an AB test of two conditions, where the success metric is looking for an increase in the number of users taking a particular action each day. The variance is hugely larger than the mean, ...
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### Interpret Interaction Effects in Negative Binomial Regression

I have two questions regarding the interpretation of interaction effects in a negative binomial regression model. The model uses the number of people arriving at a hotel per hour as the dependent ...
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### R² for a negative binomial regression model

I have been searching quite a while to find a useful way for calculating (an estimate for) the explained variance for a negative binomial regression model in R... Knowing that the "explained variance" ...
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### Can I use the Anova (type II) to test significance in my negative binomial regression?

I have fitted a binomial regression (glm.nb using the MASS package) to my data. I have two questions and would be very thankfull if you could answer any of them: 1a) Can I use the Anova (type II, ...
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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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### Concavity of negative binomial GLM

I need to estimate the log-likelihood of the negative binomial regression. I mean full log-likelihood, including the dispersion parameter. The problem is: when I start LBFGS, BFGS, or gradient ...
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### Continuous predictors for negative binomial regression

I can't seem to find a straight answer for this question. From formal coursework I've taken, it seems that Poisson/negative binomial regression require a data layout like this: Where the categorical ...
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### Nested Negative Binomial (or zero-inflated) Regression

I am currently working on methods for a thesis project. I will be modeling the outcome of disease incidence for two different diseases using negative binomial regression. It will most likely be zero-...
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### Why is the left-hand sum of negative binomial probabilities is equal to the right hand sum of ordinary binomial probabilities?

The textbook I am using states that the left-hand sum of negative binomial probabilities is equal to the right hand sum of ordinary binomial probabilities.Why is this so? The book uses the following ...
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### Test if two coefficients are statistically different in negative binomial regression in R? [closed]

I am currently working with negative binomial regressions and I would like to test whether two coefficients in the same model are significantly different from each other in R. I have read on some ...
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### What is the difference between a Zero-inflated negative binomial regression and a Heckman-two-step regression model?

The title of my question says pretty much what I'm struggling to understand: What is the difference between a Zero-inflated negative binomial (ZINB) regression and a Heckman-two-step regression model?...
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### Interpreting random effects in zero-inflated models

For context, I have a longitudinal study measuring counts of bacterial sequences in human stool collected during a dietary intervention. Initially, I was going model the change in each bacterium (...
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### When (if ever) is the sum of two dependent geometric RVs negative binominal?

Imagine you have two random variables $X$ and $Y$, you know $$X \sim \text{Geometric}(p) \\ X + Y \sim \text{Negative Binomial}(2, p)$$ I am interested in what if anything can be said about the ...
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### simple inter arrival time

I have question regarding inter arrival time. I want to simulate inter arrival time, and my distribution for number of events durring a day follow negative binomial distribution.There are many ...
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### Is the event independent?

I wanted to know if this event is independent or not? The question is as follows: In monsoon season, what is the probability that we will have a sunny day after a series of rainy days, or the ...
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### Output of a glm.nb, ratio beween Residual and degrees of freedom

Hello community and thanks in advance! I have a dataset with fish counts out of: Six years annual surveys ( so 1 survey per year) At 10 sampling points At 8 of those 10, two different depths ( 5 ...
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### Interpreting the Coefficients of a Negative Binomial Regression Analysis

I have built a negative binomial regression model in R, that looks at the relationship of between the number of times a radio ad was played (this is called TaImpacts) and the number of New Users on a ...
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### How do I analyse a negative binomial with TWO stopping critera?

I'm a first time poster looking for stats advice. I'm a biologist performing research on numerosity in hummingbirds- in more layman's terms, whether they can "count" and tell the difference between ...
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### Negative binomial-distribution as background-model: How to calculate the p-value?

I would have a question to the statistics of the following paper: Bioinformatics, Volume 28, Issue 23, 1 December 2012, Pages 3013–3020, https://doi.org/10.1093/bioinformatics/bts569 Simple summary: ...
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### Choosing the right model: Poisson, Quasi-Poisson and Negative Binomial?

 I am working in R. I am investigating the effects of weather on restaurant demand. My DV is the number of restaurant visitors per hour, my IVs are five weather variables and all other ...
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### Using T -test results to find probability of an event occurring

Given two samples, one consisting of a different number of times someone made sales calls to different potential clients who ended up buying the product. the other one consists of a different number ...
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### Modeling time to first success with dropout

I would like to model the following situation: Individuals flip coins until they get a heads. It is also possible for individuals to quit flipping/drop out of the experiment before they get a ...
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### getting negative binomial from poisson and gamma

This equation is from a statistical genetics research paper. I'm struggling to understand how they get negative binomial from the integral. x_cn is poisson and q is gamma. Is there such a rule? Or is ...
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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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### How can I tell whether this is a negative binomial distribution or binomial distribution?

A scientist inoculates several mice, one at a time, with a disease until he finds 3 that have contracted the disease. If the probability of contracting the disease is 1/6, what is the probability that ...
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### How to obtain different values of “parameter k” in a mixed-effects negative binomial model?

I have a dataset with two level factors - fertilizers ("Nitrogen" or "Phosphorous") that differed in their concentration level("...
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### Negative binomial random effects models (glmmTMB/gamm/gamm4)

Can anyone help please. Am I missing something fundamental here? I would like to test for a Cave and a Category effect in the same model, and I'd like to know if I've specified the random effects ...
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### parameter estimation with samples drawn from multiple negative binomial distribution with shared parameter

I have $N$ samples, where each sample $Y_i$ is drawn from a negative binomial distribution $$Y_i | \ell_i, \alpha, \beta \sim \text{NB}(\alpha, \frac{\ell_i}{\beta + \ell_i}), \quad i=1,\dots, N$$ ...
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### Inferences from a zero-inflated negative binomial distribution?

Frogs are generally known to spatially aggregate during egg-laying. I manipulated their egg-laying sites with different fertilizers ("Nitrogen" or "Phosphorous") that differed in their concentration ("...
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### Standardizing predictors for Neg Binom Regression

tl;dr: If I include an interaction term in Negative Binomial Regression, should I standardize the predictors? I am analyzing a very large dataset (over 60 million observations) that has the following ...
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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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### Negative binomial estimate output

I am doing a negative binomial regression: m1 <- glm.nb(Trip ~ Origin + Destination + Distance, data) I then wanted to get the predicted values to compare ...
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### GLM: How to test if an alternative predictor variable is better

I have a simple model where the expectation of the outcome variable y is proportional to a predictor variable x1. The outcome ...
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### Why and how do poisson regression and negative binomial regression preserve sum of predicted outcomes

I am using poisson regression and negative binomial regression to fit a dataset. In the meantime, I discovered that the sum of fitted values of poisson regression is exactly the same as the sum of ...
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### On average, how many trials does it take to get X successes given that successes increase the success rate?

Specific Scenario: What is the average number of trials it takes to reach 4 success in a scenario with a 9/20 success rate, where each success increases the success rate by 1/20?
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### Pearson Goodness-of-Fit Test

I am trying to compute the Pearson-Goodness-of-fit statistic for Count data to see if the mean and variance are correctly specified. I am using example data from Deb and Trivedi downloaded here: https:...
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### Computing different types of negative binomial regression

I want to compare different Count Data Models. How does one compute NEGBIN type I and NEGBIN type II in R? Which model is estimated by glm.nb()? Thanks in advance
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### 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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### Why do negative binomial regression coefficients differ by level of data stratification and coefficients from Poisson models do not?

I'm trying to understand why regression coefficients from negative binomial models are sensitive to the level of stratification of the data and regression coefficients from Poisson models are not. ...
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### 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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### How to calculate ICC for a zero-inflated negative binomial model

I did a zero-inflated negative binomial regression on some data. However, the data is nested (students within schools), and I would like to calculate ICC to make sure that we did not need to take this ...
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### Substantive Interpretation of Negative Binomial

I am trying to interpret the output from a negative binomial regression. Online, I read that we can exponentiate the coefficients to get substantively significant values. However, I know that this ...
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### Marginal Effects in R

I estimated a negative binomial regression model in R that counts the number of cyberattacks a country initiates per year. My unit of observation is country-year. Since cyberattacks are a very rare ...
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### Kruskal-Wallis and Negative binomial regression do not agree

I am comparing the number of broods made by dung beetles (Brood_Number) across three temperature treatments (Temp_Offset, a 3 ...
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### Literature request: (in)appropriateness of negative binomial for count data with an upper bound

I conducted an analysis where I used binomial logistic regression to analyze x successes in n trials (where n varies between observations) in aggregate (using the R syntax ...