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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.

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5 votes
2 answers
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Standard negative binomial regression when counts are mainly zeros?

This question must have been asked many times before but I can't find an answer. I'm getting very confused about when to use a zero-inflated negative binomial regression vs standard negative binomial ...
Picapica's user avatar
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1 answer
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When to choose GAM over GLMM and how to include random effect into GAM

This is a follow-up question to this question. Here is a description of the dataset: the outcome variable is the number of contacts per participant for two periods before lockdown and under lockdown. ...
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Covariance of multivariate negative binomial with random effects

I am fitting a negative binomial-2 regression model where there is a multivariate normal random effects term. I would like to find an equation for the covariance of two outcomes. In "the ...
Nick Link's user avatar
4 votes
2 answers
51 views

$\min\{X,Y\}$; where $X,Y$ are geometric random variables

Does $\min\{X,Y\}$ follow a geometric distribution? $X \sim BN(1,p); Y \sim BN(1,q)$ independent $$P(\min\{X,Y \}=k)=P( \min\{X,Y\} \geq k)-P(\min\{X,Y \} \geq k+1)=\sum_{n=k}^{\infty}(1-p)^{n-1}p\...
AaaBach's user avatar
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1 answer
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Relating animal sightings with land cover - poisson, negative binomial, zero inflated and then LOST

I have a number of sightings of animals in a location (an island). The sightings are opportunistic (corpses people stumble upon) and happen in different land covers. I am supposed to investigate if ...
Miren Sanov's user avatar
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28 views

Am I using the right method to model my zero-inflated data?

I have a dataset of workplace permits, sample size n=3000. The data is collected between 2012-2020, so if a permit was active some time between 2012-2020, I included it in my analyses. My exposure of ...
user9410's user avatar
0 votes
1 answer
22 views

Underdispersion handled with negative binomial distribution? [duplicate]

To get a more flexible model than Poisson regression, one can choose the negative binomial distribution instead for modeling with $E[y] = \mu$ and $Var(y) = \mu + \frac{1}{ \theta} \mu^2$. As a ...
Marlon Brando's user avatar
1 vote
2 answers
41 views

Calculate combined confidence interval of two variables in a negative binomial model (in R) [closed]

I have a multivariable negative binomial model in R for which I want to combine two variables: Variable 1: binary variable (no/yes) Variable 2: continuous variable (0-3) I want to calculate ...
femkev's user avatar
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2 votes
1 answer
58 views

Negative Binomial Regression for repeated measures ,daily for one week

I have a dataset of 2,000 subjects, each providing daily social contact data for one week (14,000 observations = 2000 subjects * 7 days). I aim to describe the number of contacts using variables such ...
Jong-Hoon Kim's user avatar
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0 answers
25 views

Construction of Dirichlet multinomial from independent negative binomials

I have a dataset with ISO3 country code, Year (from 2010 to 2019), Causes of death category (24 categories in total) and number of deaths. The sum of deaths across causes is fixed. My goal is to ...
WellWellWell's user avatar
7 votes
3 answers
243 views

biased MLEs in negative binomial models

I found the maximum likelihood parameters of negative binomial models are biased. An example code is provided below. Is this normal? Are there ways to obtain unbiased estimates? ...
quibble's user avatar
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1 answer
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Visualizing restricted cubic splines in glm.nb

I am trying to visualize the relationship between a continuous variable ("marker") and a count variable ("count") using a negative binomial regression with a restricted cubic ...
Fabian's user avatar
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0 answers
30 views

Low VIF in conditional model but high in zero-inflated model

I am using glm ZINB to make models that predict abundance of frogs based on observations from 57 sites. I used the check_model function from the performance package and it shows that the best model ...
Marco Lassandro's user avatar
2 votes
0 answers
44 views

Are there known bounds for the median of a negative binomial distribution based on its parameters?

This seems like an innocent enough question to me, but I could not find a satisfactory answer when I did some digging. The binomial distribution has a closed form median and the Poisson distribution ...
ricewhitlam's user avatar
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Am I Doing Things Right? / negative binomial test

I have a dataset consisting of social media comments about a particular context from 1999 to 2024.The topic titles of the comments were annotated into two categorial variables = 0 and 1. I am aiming ...
berk's user avatar
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0 answers
26 views

Model failed to converge using glmer

My dependent variable is actigtraph measurements measured every minute for 55 individuals (count data- right skewed, most values at 0). I have around 1.2m rows. Here is my simple random intercept ...
Anshika's user avatar
2 votes
0 answers
29 views

Reimplementation of MASS::glm.nb with fastglm [closed]

I'm trying to make a simple implementation of MASS::glm.nb via fastglm. The idea is to get the same output but to make the ...
Giovanni Tinervia's user avatar
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0 answers
37 views

Does the negative multinomial distribution have a defined CDF?

I have a process that receives categorically distributed random inputs of 5 different types. The 5th type is considered "bad". If the process receives 4 bad inputs before receiving at least ...
ZPears's user avatar
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30 views

Negative Binomial GLM - Overflow in the link function

I am trying to create a GLM to model some count data. I am using the pymc package in python. The set up is what I believe to be the usual set up: $$Y \sim NB(\mu,k) $$ $$E(Y\vert\mathbf{X}) = \mu $$ $$...
TNoms's user avatar
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11 views

Continuous mixture distribution

I am currently working on the derivation of the negative binomial distribution as a result of a continuous mixture of Poisson and Gamma distribution for regression purposes. To obtain the entire ...
Marlon Brando's user avatar
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0 answers
40 views

glmmTMB ZINB model non-convergence

I am looking for help with fitting a ZINB model with mixed-effects. The model which I intend to fit contains a random-intercept (three variables/terms denoting the nested, hierarchical group structure)...
Suhas Bharadwaj's user avatar
2 votes
1 answer
25 views

Count Data Dependent Variable

Just a quick one - I am planning on running a negative binomial distribution to test the time spent at the gym in a week, against a series of controls. I just wanted to double check - would the number ...
Vito's user avatar
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0 answers
36 views

Negative Binomial SPSS Error

I was running a negative binomial regression in SPSS and received the following message: The maximum number of step-halvings was reached but the log-likelihood value cannot be further improved. Output ...
Vito's user avatar
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0 answers
31 views

Is this suitable for Negative Binomial Regression?

I am using SPSS to run a negative binomial regression for my research project. My dependent variable is 'Number of Days Went to the Gym' in a week, and my independent variable is income (along with a ...
Vito's user avatar
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5 votes
1 answer
226 views

SPSS R^2 for Negative Binomial

I am running a negative binomial regression in SPSS and wondered if there is any way to display R^2 statistics, as would be the case if binary/linear regression was conducted?
Vito's user avatar
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4 votes
1 answer
164 views

Running a Negative Binomial Regression with Overdispersion

I am not an expert on SPSS but have been developing my skills and believe I should run a negative binomial regression on my data, though I am not certain. I am testing the number of days people go ...
Vito's user avatar
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0 answers
19 views

Missing predictor variable in GLMM.nb outcome

After running the model: ...
Adrianna Elihu's user avatar
0 votes
1 answer
39 views

GLMM with negative binomial- narrowing down variables & choosing a model

I'll start by saying apologies for perhaps not wording things correctly, as stats is not my first language (lol). Please let me know if there is any other info I need to provide to make this easier to ...
Adrianna Elihu's user avatar
2 votes
0 answers
32 views

Choosing between Negative Binomial, Zero-Truncated NB, and NB with Arithmetically Altered Outcome (SAS)

I am modeling longitudinal Days of Pill Supply with predictors Number of Rx's and Patient Race. I was not able to use linear regression (proc reg or proc glm) because of heteroscedastic residuals, so ...
L.S.'s user avatar
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2 votes
1 answer
83 views

Multinomial distribution approach as negative binomial?

I was asked to solve a problem, following the multinomial distribution (if you think is the correct approach, which I actually think it is). I paste the whole problem just in case I am approaching, ...
Javier Hernando's user avatar
5 votes
1 answer
68 views

Questions around modelling arrival process of randomly sized groups

I have the following situation: I'm trying to model groups arriving to some location by some process. I assume the distribution on some interval $T$ is a Gamma-Poisson mixture where $\Lambda \sim ...
BeechAndBirch's user avatar
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0 answers
28 views

Applying negative binomial distribution for weighted events [duplicate]

I'm trying to model the age of inventory at time of sale, where a given sale (say, for \$10,000 worth of a particular product) might be fulfilled with \$5,000 of stock that is 1 month old, \$3,000 ...
Scott Deerwester's user avatar
0 votes
0 answers
37 views

Post-hoc tests of interaction for a negative binomial regression with survey weights?

I ran a negative binomial regression with survey weights using the R package survey and the function svyglm() and observed a ...
Chernoff's user avatar
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0 votes
1 answer
59 views

Constructing a one-sided hypothesis test for joint probabilties of negative binomial distributions

I am conducting research on Codling moth population/trap capture models. The end goal is to have a hypothesis testing model that will provide whether or not (at some significance level $\alpha$) the ...
Pacific Bird's user avatar
0 votes
0 answers
13 views

NB regression and LAG variable X

I'm doing a time series analysis, and I want to fit a negative binomial regression model. I did a GRANGER analysis that told me that the LAG of X explains Y better than the LAG of Y. And in the ...
Rafael Nicolino's user avatar
4 votes
2 answers
102 views

How do I work out the significance of main effects in negative binomial models with more than two factors?

I am trying to look at how the number of events X is affected by the three factors A (4 levels), B (2 levels) and C (2 levels) using a negative binomial model as follows: ...
Insect_biologist's user avatar
1 vote
0 answers
63 views

Equivalent of R-squared in negative binomial regression

In my study, I experiment with fixed and mixed effects negative binomial regression to my data (in R) as the response variable is a count variable. I have read somewhere that unlike in the case of ...
dysko's user avatar
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4 votes
1 answer
80 views

Requirements for negative binomial regression

In my study, I experiment with fixed and mixed effects negative binomial regression to my data (in R) as the response variable is a count variable. Normally I should use Poisson regression but (and ...
dysko's user avatar
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0 votes
0 answers
27 views

Is it possible to run a zero-inflated negative binomial model with complete separation? [duplicate]

I am trying to analyze how the number of events Y is influenced by three factors A (4 levels), B (2 levels) and C (2 levels) and the interactions between the three. Initially trying a poisson ...
Insect_biologist's user avatar
2 votes
1 answer
56 views

Predictive capacities of Generalized Linear Models and significance

I have the following data ...
GiorgioS's user avatar
0 votes
0 answers
20 views

Incomplete formula for the glm negative binomial

My data is about the number of insects that go to treatment 1 or treatment 2, and I have the factor place, with four levels (places). Each place has a treatment and ...
Yahana Aparicio's user avatar
4 votes
2 answers
303 views

Taking the limit of a Beta Distribution to yield the Gamma Distribution

The Poisson Distribution may be obtained from the Binomial Distribution by keeping $\lambda = np$ fixed and taking the limit as $n \rightarrow \infty$. Similarly, the Gamma Distribution may be ...
SSD's user avatar
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0 answers
25 views

Clustering and segmented regression interrupted time series analysis

I would like to perform an interrupted time series analysis to look at the impact of the pandemic on cancer incidence using individual level data. I plan to use a negative binomial segmented ...
user405452's user avatar
3 votes
1 answer
74 views

transforming a continous respond variable into a discrete one

I am visually estimating fish length underwater to convert it in fish biomass by means of proper length-weight relationships. Obviously, my accuracy is not perfect. When making hypothesis about ...
Jose's user avatar
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0 votes
0 answers
24 views

How to construct confidence intervals for difference of means in logs

I have estimated an OLS model and a Negative binomial model of ln housing search (ln S) per unit (for instance, the average number of visitors per house or bidders per house) as a function of ...
Mari Mamre's user avatar
2 votes
2 answers
140 views

From overdispersion to underdispersion: comparing linear regression models with DHARMa

I have been investigating the relationship between the occurence of certain weather phenomena and time. To aid me in evaluating the fit of my (simple linear-regression) models, I have been using the ...
Sargnagel's user avatar
0 votes
0 answers
33 views

Can I use the Negative Binomial distribution to calculate the max number of trials where I have less than X fails with some confidence?

Thank you in advance for any help. I am trying to compute the maximum number of times I should expect to attempt a Bernoulli trial to keep my number of fails (with probability of failing $p$) under ...
askingforwork's user avatar
2 votes
1 answer
174 views

The sum of two Negative Binomial variables doesn't follow a Negative Binomial

I assume that the number of home corners and away corners would follow the Negative Binomial Distribution and I expect that these two variables have the same parameter ...
Juan's user avatar
  • 57
2 votes
0 answers
45 views

Can a covariate also be a random effect in glmmTMB model with ar1 [closed]

I have data consisting of catches of insects at weekly intervals over 2 years, repeated with the same methods at the same location 3 decades later. My main question is, have numbers (total and for ...
IMH's user avatar
  • 41
2 votes
1 answer
62 views

Distribution of a conical combination of n poisson variables?

Does a conical combination of n Poisson distributed variables have a closed-form distribution (linear combination with nonnegative coefficients)? I know that the sum of random Poisson variables would ...
Tom Wenseleers's user avatar

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