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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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Visualizing 2D data when one dimension is discrete and the other continuous

I have some (synthetic) stochastic data generated from a model with two parameters (e.g., I'm generating many numbers from a negative binomial distribution with parameters $n$ and $p$ --- that's close ...
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10 views

Is there a single discrete distribution that handles over and under dispersion? [duplicate]

I have some count data I am trying to model. The variance is very close to the mean, so the Poisson distribution for the entire data set seems like a good starting point. I have done and it seems to ...
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71 views

UMVUE- geometric distribution where $X$ is the number of failures preceding the first success

$X_1, \dots, X_n$ iis geometric: $P(X=x) = (1-p)^{x}p$, $x=0,1,2, \dots$ My Attempt: $T=\sum_{i=1}^n X_i$ is a sufficient statistic $W= \begin{cases}1 & X_1= 0,\\ 0 & X_1\neq 0\end{cases}$ ...
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How to compare approximate Bayes Factors (BIC) with glm.nb? (R stats)

I have a situation where I would like to write up an analysis where the statistical significance is non-significant. I wanted to be able to accept the null hypothesis instead of merely 'failing to ...
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47 views

Is the methodology for my undergrad dissertation sufficient - should I use a hierarchical negative binomial model instead, despite beginner ability?

As said in the title, I know almost nothing about statistics. My hypothesis for my dissertation is that UK Members of Parliament with a larger margin of victory will do less work than those with a ...
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14 views

Handling quasi-perfect separation in a zero-inflated negative binomial regression in R

I want to run a zero-inflated negative binomial regression in R, but one of my variables exhibits quasi-complete separation and throws errors for both the negative binomial and logistic pieces. I've ...
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21 views

Multivariate (Multi-responce) for negative binomial (GLM) in R

I developed a multivariate linear regression using lm() function in R. However, I am having trouble coding a Multivariate model in R for glm(), especially for the negative binomial. Can anyone point ...
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What are recommended practices to avoid overestimation of size/dispersion from small samples of negative-binomially distributed data?

I want to estimate mu and size/dispersion accurately for a large number of small samples (n = 6-8 is typical). When I try to do maximum-likelihood inference (or related, Bayesian inference with ...
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1answer
90 views

Trouble modeling zero-inflated data. Estimates and standard errors are off with GLM, GLMM, and ZI models

I conducted a study looking at the attraction of different species of insects to 5 different chemical treatments (I have had other issues with this dataset explored here and here). This experiment ...
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1answer
34 views

mixed effect model?

I have 365 days of bike sharing demand data for 15 stations. I am thinking of taking each day data as a data point (n=365*15=5475) and relate daily weather variable as well as land use variable. The ...
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39 views

Mixed effect zero inflated negative binomial model: “the leading minor of order 1 is not positive definite”

I am having trouble fitting a mixed effect zero inflated negative binomial model to my data using the GLMMadaptive package: ...
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1answer
54 views

Relation between binomial and negative binomial

I was reading on negative binomial from a Statistics textbook and came across this portion on probability relation between binomial and negative binomial. $Y$ refers to the number of trials required ...
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10 views

the importance of estimating correctly the dispersion parameter in hypothesis testing

I am reading an article, which is related to negative binomial model in estimating the dispersion parameter. https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0081415 The author ...
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36 views

How are these two parametrizations of the Pascal PMF related?

On Wikipedia, the Pascal PMF is written as $$p(k)=\begin{pmatrix}r+k-1\\k\end{pmatrix}p^k(1-p)^r\tag1\label1$$ where $r$ is the number of failures before the $k$th success and $p$ is the success ...
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1answer
31 views

Should I include offset in null negative binomial model for comparing to full model?

I'm modeling how various landscape and ecological factors affect the I'd like to evaluate how well my negative binomial model performs over the null. I've specified an offset variable in my model to ...
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25 views

Gradient of parameterized negative binomial generator?

I have a function negativeBinomial(μ,σ) that generates a random value X that follows the negative binomial distribution of mean $...
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1answer
25 views

Offset term in negative binomial regression

I am fitting a simple negative binomial regression model with (Yearly cancer death ~ Offset (Size of population) + Age + Household income). I used the offset term because I want to compare the yearly ...
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1answer
33 views

Transfering the approach of GLM/GLM.NB to FEGLM in R to find the best dispersion parameter

I would like to analyze my dataset with around 1 million observations and 10 thousand fixed effects with a negative binomial regression model. Due to the high number of fixed effects I cannot apply '...
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1answer
25 views

Negative Binomial Substitute for Poisson Applied to NYC Crime Data

I'm reading these questions and answers (http://study.sagepub.com/sites/default/files/chapter4.pdf) and am confused about 4.2.4 - 4.2.6 I agree that the Poisson model developed earlier is not a good ...
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2answers
105 views

Choosing the optimal theta / dispersion parameter for negative binomial regression (glm / glm.nb) in R

I am applying a negative binomial regression to my data in R. For this, I use the package MASS and have two different ways to calculate it: ...
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5 views

Variable selection in Bayesian spatio-temporal count regression

I am estimating a Bayesian spatio-temporal Poisson model. I have a relatively large set of explanatory variables (20ish) and each time I run the model it takes a few hours to complete. I have seen ...
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20 views

Distribution/analysis method for small dataset with many small/zero values

I have a relatively small dataset (160 observations), of which a very large number of values for response variables are zero or very small (e.g., 114/160 values are 0; range 0-4250, with only 11 ...
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1answer
25 views

Incomplete block design analysis

I have 4 treatments (6m, 12m, 24m, 40m) in 3 blocks, but all treatments are not replicated in these blocks: 6m, 12m, 24m are in Blk1 and Blk2 and Blk3 consist of only 34m (control plot) and 6m. How ...
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1answer
45 views

Mixed-effects Generalised Linear Model (GLMM) to detect significant differences in bird observation data

I am trying to analyse a set of bird count data associated with an environmental impact assessment I am running, but require experts to get this right. I am unsure how to formulate the model and ...
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Sensitivity and Specificity of gaussian and negative binomial glm family

I am dealing with count data that is over-dispersed and hence I consider using the negative binomial family (with glm()) instead of the gaussian family, as the link function. To find out the ...
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1answer
74 views

Hierarchical Bayesian Negative Binomial model with Gamma prior on mean

I am interested in deriving the full conditional for the mean parameter in a Neg-Binomial model with a Gamma prior on the mean, as such: \begin{align*} Y|\lambda,\phi\sim & NB(\lambda,\phi)\\ \...
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120 views

Overdispersion parameter in R's glmmTMB

I am using R's glmmTMB for modeling negative binomial mixed effects. In the output, I see the following line : ...
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33 views

Negative Binomial Regression Coefficients and Std. Errors in R

I've done my due diligence in looking throughout crossvalidated to look for a solution but instead have found very different approaches. I'm running a negative binomial random-intercept model using ...
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2answers
284 views

Difference between geometric distribution and negative binomial distribution

How do I differentiate between a problem of geometric distribution and that of Negative Binomial Distribution? Both include something around first success or failure. I'm confused.
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89 views

Conditional probability of Negative Binomial R.V. given the SUM of its values

Suppose $\{z_{ij}\}$ are independent Negative Binomial random variables with means $\{\mu_{ij}\}$, with $i=1\dots I$ and $j=1\dots J$. How do you find the (expectation of) conditional probability ...
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21 views

Hurdle models and word count

Question: why negative binominal part of hurdle model does not provide coefficients for intercept and word count? I have counted positive emotional words (Y) in some conversations that have a ...
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2answers
82 views

Regarding glm.nb() and my parameter

I have been doing a negative binomial regression model using the following code My my estimate here comes out as 3.48. (the exponential of the intercept). The data was taken randomly (with set seed) ...
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1answer
114 views

Variable Selection for Negative Binomial Regression

First off I apologize, that I cannot share the code or details about the variables for this project. I am new to statistics and am working on a project using count data. I want to make sure I am going ...
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1answer
43 views

Intensity function in Poisson random effect model

I have a somewhat general question about intensity functions in Poisson random effect models. Consider the Poisson random effects model in which conditional on a random effect $u$, an individual ...
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1answer
47 views

Negative Binomial Regression: Offset Variable and Dispersion Parameter

My case is that previously it's assumed that the counts of events follows a negative binomial distribution, and the annualized exacerbation rate is 1 with a dispersion parameter of 1.5, and all 500 ...
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1answer
52 views

PROC GENMOD Negative Binomial doesn't predict zeros

I am using PROC GENMOD with time series data, I have tried to work with Negative Binomial, Poisson, GEE and Zero Inflated Poisson, but in each case when I score my validation dataset, I am getting ...
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24 views

Goodness of fit for zero truncated negative binomial model

I have calculated a zero-truncated negative-binomial model using glmmadmb, and also vglm, in R. I need to report some measure of goodness of fit for this model. I have already done cross validation (...
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1answer
206 views

How do I interpret a negative binomial regression with categorical predictor?

I am trying to interpret R output for a negative binomial regression. Below is my output. I'm trying to infer how much my predictor (socfrend_bin) affects my ...
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1answer
155 views

Poisson distribution - Number of accidents

I need help with this probability problem. The number of fatal car accidents that happen in a specific region follows the Poisson distribution with a rate of 0.5 fatal car accidents per day ...
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24 views

Offset in NB model produces contradictory results to original data

My (example) data frame is rather simple. I would like to know if there is a difference in numbers between the factors (n=2) within variable X. ...
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1answer
166 views

Exemplar MLE for negative binomial?

I recently compared MLE estimates for a negative binomial fit using two different pieces of software, and got different results. I'd like to determine which (if either) is correct. To do that, I'd ...
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1answer
83 views

Would it be more appropriate to use negative Binomial regression instead of Poisson regression if my sample variance is greater than my sample mean?

My response variable $y_i$ denotes the number of articles produced by journalist $i$ in the last two years. It is a count variable with fixed exposure hence why I chose to use Poisson regression. I ...
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11 views

Calculating significance threshold from one-tailed distribution

I have a total of 460 samples, in which I have calculated some statistical value, such that I get a left skewed distribution with a right tail, roughly equivalent to a negative binomial distribution. ...
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68 views

Compairing the fit of quasi-Poisson and negative binomial models

Is there any way to compare the fit of quasi-Poission and negative binomial models in R?
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60 views

Negative Binomial having count data with an upper bound

The general statement is that you cannot use Negative Binomial or Poisson with count data with an upper bound, which makes sense. However, in my case my count data is always much lower than the upper ...
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1answer
236 views

Reporting glmer.nb Results

I'm running a mixed negative binomial GLM that looks like this: Niche2 <- glmer.nb(log_density ~ height * factor(Year) + (1 | Grouping), data = NicheData2) ...
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38 views

Why there are not (long tail) alternatives to dirichlet-multinomial (while there are for posisson-gamma)

While there are a lot of long tail alternatives to poisson-gamma (negative binomial), for example (Source) I haven't found any work on replacing the dirichlet distribution with a more long tailed ...
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32 views

Compairing quasi-Poisson and negative binomial fits in R [duplicate]

Are there any R functions that allow you to easily compare quasi-Poisson and negative binomial models to determine which error distribution is more appropriate for your data? Or - does this require ...
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0answers
140 views

Why can't you fit a quasi-Poisson in `lme4`? [closed]

Is there a philosophical reason why lme4 does not allow you to fit a quasi-Poisson model while it will allow you to fit a negative binomial model? I do not see any reason why any glmm package should ...
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2answers
45 views

Predicting Negative Binomial response when some observations contain no success

Problem description: I am attempting to model the number of attempts required in order to make event $Z$ happen. Each day we make $k_i$ attempts with setting $X_i$ (a vector) in an effort to make $Z$ ...