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

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3
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1answer
29 views

Use law of total variance to find unconditional variance of overdispersed Poisson?

First, I need to prove that the distribution of a RV X, where X|lambda ~ Pois(lambda), and lambda ~ gamma(a, B), is a negative binomial. I know that it is, but why negative binomial instead of another ...
0
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1answer
16 views

Does and 95% CI containing 1 imply no difference in IRR calculations in the same was as in OR calculations?

My understanding is that with an odds ratio (OR) that a 95% CI containing 1 means that there is no difference between the odds of something occurring between groups. I wondered if this holds true for ...
0
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0answers
10 views

Bootstrap of parameter estimates and confidence intervals (hurdle model)

Think you can help with this. I´ve run a set of candidate hurdle models on insect abundance data with pscl package for R. These models had an abundance part with a truncated negative binomial ...
2
votes
2answers
42 views

How to evaluate goodness of fit for negative binomial regression

I'm trying to fit a model estimating waiting time using negative binomial regression, but I'm not sure how to assess the goodness of fit for my model. I would like to compare the negative binomial ...
0
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1answer
30 views

correct use of Negative Binomial with a Geometric distribution in a mixed model (glmmPQL)

I am trying to fit a NB GLMM with a gemoetric distribution. I have come across very little information on this form of regression. And would like some pointers/reasurance. some literature is ...
2
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0answers
39 views

does the equivalence of Poisson and conditional logit models hold for fixed effect panel data and negative binomial models?

Guimaraes et al. (Rev Econ Stat, 2003, 85/1) describe the conditions under which the results from poisson regression models and conditional logit models are equivalent. I am trying to find out whether ...
2
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0answers
46 views

Basic idea of zero inflated two part models(hurdel) and application to big data (machine learning)

I'm currently working on the data which has 90% 0s in response variable. Based on my research, it seems zero inflated models could be a solution to this. However, while I was reading related ...
0
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0answers
52 views

R² (squared) from a generalized linear mixed-effects models (GLMM) using a negative binomial distribution

I try to compute the marginal and conditional R² for a GLMM using a negative binomial distribution by following the procedure recommended by Nakagawa & Schielzeth (2013) . Unfortunately, the ...
2
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0answers
123 views

Estimating abundance using non-normal count data

I have sample counts of $n=20$ or $n=7$ taken from right-skewed and zero-inflated populations. The challenge in each case is to use the sample to estimate the total count in that population. Each of ...
1
vote
0answers
19 views

Limits of zero-inflated negative binomial in % of zeroes

What are the limits of a zero-inflated regression? Specifically, if more than 80% of the data is zeroes, is the ZINB still valid? What is a good rule of thumb or educated way to understand the right ...
5
votes
1answer
61 views

Zero inflated negative binomial with selection

I am looking for a Stata (or R/Matlab if there's no Stata) implementation of the model described by Greene (1994) (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1293115). It is essentially a ...
0
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0answers
11 views

comparing same negative binomial models built with subset data

I have a dataset made our of several stacked datasets (one for each state). I want to check whether a zero inflated negative binomial model with data from an individual state is different from the ...
1
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0answers
53 views

GAM with negative binomial and temporal autocorrelation

I want to fit a GAM in R. My data are negative binomial. Plus they have a temporal autocorrelation. ...
0
votes
1answer
28 views

Controlling for variables in negative binomial regression

I would like to run a negative binomial regression, but also controlling for one of the variables. Similar to what you would do with a hierarchical regression. I am trying to predict violence (never, ...
1
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0answers
21 views

Leave-one-out cross-validation for negative binomial

I've just started working with the GLM negative binomial and I was wondering if it's possible to carry out a leave-one-out cross-validation for negative binomial GLM as I'm having troubles doing it ...
6
votes
1answer
87 views

In a Poisson process measured with some efficiency, is the measured count still Poisson?

Situation: Say I have a Poisson process, like radioactive decay, producing R particles per second. I measure with a detector. There is a probability P that a particle will be detected by the ...
2
votes
1answer
19 views

I got a good OLS fit for integer variables, do I still need to use count data methods?

First of all, I'm not a statistician, but I'm teaching myself some methods I require for a project I'm doing now. I have a 2D dataset of N observations. For the ith observation, the first entry is ...
1
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0answers
33 views

Can i use a mixture model for when I have an omitted variable?

I plan to fit a GAM or GAMM. There is one categorical variable which I think is important for explaining Y (or Y*), but it is not in my dataset - it is measurable but has not been measured. Can I use ...
8
votes
2answers
323 views

Why are Pearson's residuals from a negative binomial regression smaller than those from a poisson regression?

I have these data: set.seed(1) predictor <- rnorm(20) set.seed(1) counts <- c(sample(1:1000, 20)) df <- data.frame(counts, predictor) I ran a poisson ...
0
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0answers
55 views

fisher information matrix of Negative Binomial distribution

can anyone show me how to find the Fisher information matrix for negative binomial distribution, if I parameterize the Negative Binomial distribution using parameters mean and size. Thank you!
2
votes
2answers
231 views

Why do ANOVAs and GLM (negative binomial model) give different results for interaction effects?

In my study, children repeat sentences and I count the errors (DV = error rate). Children are divided into two groups (Group factor), and there are two different types of sentences (Condition factor). ...
3
votes
1answer
161 views

Zero-inflation on steroids: choose among Poisson, negative binomial and zero-inflated regressions

I am struggling to fit alternative count models into my data. I guess my problem is just too many zeros. This is my data ...
1
vote
1answer
79 views

Negative binomial distribution fit

I am trying to fit a negative binomial distribution, in R, to my over dispersed data (out of 20 ,14 samples are 0, and rest are less than 5). The mean is $-0.8$ and ...
2
votes
0answers
151 views

Hyper-prior for negative binomial in hierarchical model using JAGS/BUGS

Below I'm using a negative binomial because it is more flexible than a simple poisson model. The data are counts $y$ of events for 16 individuals $x$. There are 14 counts (i.e. counting periods) for ...
3
votes
2answers
60 views

Does the estimated overdispersion parameter of Negative Binomial depend on mean

Negative Binomial distribution can be parameterized using mean, $\mu$, and overdispersion $\psi$, so that the variance of NB is $\mu + \frac{\mu^2}{\psi}$. We know there is no analytical solution for ...
3
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0answers
43 views

Evaluate deviation from negative binomial model

I'm trying to figure out how to determine to what extent a sample deviates from a negative binomial model fitted to a larger population. As an example, I generated counts of doctor visits for a ...
2
votes
0answers
125 views

Standardizing count variables in panel data with overdispersion - R or Stata

I'm running a regression where the dependent (response) variable is a highly dispersed (slightly zero-inflated) count and the explanatory (independent or predictor) variables are continuous, counts as ...
3
votes
0answers
71 views

Error in fitting negative binomial regression model in R when replicating published results (works in Stata)

I'm trying to replicate the results of the first model of this article: Hultman, Lisa, Jacob Kathman, and Megan Shannon. 2013. “United Nations Peacekeeping and Civilian Protection in Civil War.” ...
0
votes
1answer
27 views

Interpreting ZINB - inflation model non-significant

I have a zero-inflated negative binomial model to a dataset (n = 47) with a over-dispersed dependent variable (...
1
vote
1answer
77 views

Parametrization of Gamma and Negative Binomial in R

I have some Poisson data {${y_1,...,y_n}$} and a Gamma prior, and I wish to construct a predictive posterior distribution. As I understand, if my Gamma hyperparameters are $\alpha$ (the prior number ...
1
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0answers
116 views

Analysis of rates and post hoc test with offset variable using glmer.nb

I am investigating variation in pollinator visitation rate (number of visits per inflorescence) with treatment and time category as fixed factors. Block is a random factor. Following Zuur et al. ...
1
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0answers
55 views

Comparison between normal glm and glm.nb regression with quadratic term?

Let's say I have a function to simulate data for negative binomial regression: ...
1
vote
1answer
58 views

Estimating Negative Binomial Regression Model

It is easy to estimate a Poisson regression model using the Newton–Raphson Iterative Technique as it only involves one parameter (mu). However, I am unable to understand how a negative binomial ...
1
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0answers
45 views

Exp(B) value outside 95% Wald Confidence Interval

I ran a negative binomial regression on some count data using SPSS. The intercept had an Exp(B) value below the lower limit of the 95% Wald Confidence Interval. I've never seen this happen before ...
1
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0answers
88 views

Negative binomial distribution mixture model with R

I have two data vectors of observed count data: $A$ and $B$, where count $A_n$ and $B_n$ refer to the same observation point. $A$ is assumed to follow a negative binomial distribution. $B$ is assumed ...
5
votes
0answers
77 views

How can one test the assumptions of a zero-inflated negative binomial model in R?

I have fitted a zero-inflated model with a random effect using a negative binomial distribution in R, using the function glmmadmb. This is due to a large number of zeros and over dispersion. For a ...
4
votes
2answers
213 views

extremely left-skewed response variable - how do I model this dataset?

This is a histogram showing my response variable. The response is # (or proportion? or percent?) of aphids eaten off of cards in fields, to model predation by natural enemies. Predictors: fixed ...
0
votes
0answers
61 views

What are the potential problems associated with using negative binomial regression with random effects?

Are there any major potential problems with using negative binomial regression (xtnbreg) with random effects and lagged dependent/independent variables. (Time-series cross-section data) I'm analyzing ...
2
votes
0answers
30 views

Exposure in Negative Binomial regression and other distributions

For a Poisson regression we can model exposure $\epsilon_i$ in observation $Y_i$ as $Y_i \sim Poisson(\epsilon_i*\lambda)$. For instance, in a Poisson regression, if we observe: $y = \begin{bmatrix} ...
3
votes
0answers
334 views

Trouble finding good model fit for count data with mixed effects - ZINB or something else?

I have a very small data set on solitary bee abundance that I am having trouble analysing. It’s count data, and almost all the counts are in one treatment with most of the zeroes in the other ...
3
votes
1answer
161 views

How do you estimate the predicted probability of an integer value from a negative binomial regression equation?

I'm trying to estimate the predicted probabilities of an observation being a particular integer, $y$, after a negative binomial regression model. Long's Regression models for categorical and limited ...
0
votes
1answer
128 views

Non-significant p-values for factor levels with only 0s in negative binomial glm using glm.nb() in R

I am trying to fit a negative binomial GLM to fish catch data with month of the year (factor) as my explanatory variable. I have selected the month with the greatest number of catches as my reference ...
0
votes
1answer
50 views

Model Averging for Negative Binomial GLMM in R

Ive been trying to find a way to average negative binomial GLMM using MuMin R Package but it seems not to work for negative binomial GLMM, any alternatives? thanks in advance!
1
vote
0answers
63 views

Fit Negbin glm model with autoregressive correlation structure

I am attempting to estimate the effect of various variables on the time-series of counts of reported cattle stillbirths. We investigate the effect of day-of-week, month, holidays etc…and also the ...
3
votes
1answer
144 views

Quasi-poisson or negative binomial regression with continuous dependent variable?

My dependent variable is originally count data. Because of several corrections it became continuous variable (originaly my data are pellet-group counts (for estimating deer density), corrected for ...
2
votes
1answer
130 views

Proportion as Dependent Variable or Control for the Denominator in Regression Model

I am a little confused as to which model specifications to use for my question. I have number of technological failures (positive count variable) as dependent variable but I am supposed to control ...
5
votes
0answers
133 views

Negative binomial jeffreys prior

The negative binomial distribution is NB($m,r$), $$\Pr(X = k) = \left(\frac{r}{r+m}\right)^r \frac{\Gamma(r+k)}{k! \, \Gamma(r)} \left(\frac{m}{r+m}\right)^k \quad\text{for }k = 0, 1, 2, \dots.$$ I'm ...
0
votes
0answers
25 views

How can I properly relate the dispersion parameter to other estimated variance parameters?

In a negative binomial model, could I treat the dispersion parameter as an estimate of the residual variance? In other words, could I do the following with the dispersion $D$: $$ \sigma^2 = \ln(\mu + ...
1
vote
2answers
117 views

Negative Offset in Rate (Poisson or Negative Binomial) models

I have a dataset that contains: the counts of successes, $Y_i$ the length of observation, $\text{length}_i$ few predictors, $X_1, X_2, \text{etc}$ Since the counts are observed at different ...
0
votes
2answers
121 views

Mixture of Poisson and negative binomial

I'm trying to fit a Poisson and negative binomial distribution to my data and compare the two; but the problem is that the Poisson fails to capture the overdispersion and the negative binomial seems ...