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

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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 ...
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28 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.” ...
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1answer
11 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 (...
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1answer
38 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 ...
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16 views

Assessing the accuracy of prediction (count data with few values)

I am using three different models (NB2, Poisson, hurdle) to construct a prediction function for the count data with values varying from 0 to 7 (77,93%; 15,91%; 4,15%; 1,33%; 0,51%; 0,12%; 0,04%; ...
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10 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. ...
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31 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: ...
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1answer
46 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 ...
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21 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 ...
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44 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 ...
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32 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 ...
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2answers
94 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 ...
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38 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 ...
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23 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} ...
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136 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 ...
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1answer
79 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 ...
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1answer
65 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 ...
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14 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!
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34 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 ...
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1answer
91 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 ...
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1answer
71 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 ...
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92 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 ...
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15 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 + ...
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2answers
78 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 ...
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2answers
92 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 ...
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2answers
95 views

Likelihood for negative binomial distribution

One of the parameterization of 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 ...
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1answer
63 views

Least Squares Regression in Stata

Can anyone explain how Stata computes the least squares parameters with a single explanatory variable - what algorithm Stats uses to compute the parameters. Actually I want to understand the ...
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2answers
67 views

Repeated Measures GLM / restricted permutations

I have a question regarding repeated measures and GLMs: Suppose i have counted the abundance of some species in lakes at different time points - every lake received a different treatment at time = 0. ...
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31 views

How to specify a repeated-measure random effect, and a nested plot-in-stand in a glmm.admb nbinom?

I'm not sure my glmmadmb syntax correctly specifies: that plots(2,184) are grouped or blocked within stands(24-26 per period), and there are repeated measures -- 3 winters and 3 summers on the ...
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36 views

How to estimate the overdispersion of a negative binomial distribution?

Suppose a data set is from a negative binomial distribution, Can anyone tell me how can I estimate the overdispersion parameter using R?
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1answer
108 views

Undefined real result in a zero-inflated negative binomial

I have run a zero-inflated Poisson model in WinBUGS without problems, and now I am trying to run its equivalent negative binomial. However, I get an "undefined real result" trap message over and over. ...
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44 views

How to justify using a gamma distribution for biological image analysis

I am trying to characterize objects within the nucleus of a cell. These objects are brighter than the background, and when I remove the background and map the frequency distribution of the objects I ...
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1answer
92 views

Negative Binomial “Process”

I wish to model the number of bugs caused by software development. This is intuitively sort of a Poisson process, however it is overdispersed. One thing we can do in this case is to use a negative ...
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51 views

Negative binomial regression

In a specification where negative binomial regressions are estimated, can the coefficients be interpreted directly as in the OLS case?
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1answer
103 views

Intuition for Gamma-Poisson / Negative Binomial

I have a data set which intuitively seems Poisson-like, but it's overdispered. So I'm investigating negative binomial. From this question and this page I understand one way of viewing this is to ...
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54 views

Is there anything special about Gamma distribution with the shape parameter k=e?

Is there any unique property of $\mathrm{Gamma}(k=e, \text{ scale})$ or a Negative binomial distribution with $r=e$? Here, $e$ is Euler's number, $e \approx 2.71828$. The reason I'm asking is that ...
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36 views

Comparing negative-binomial and poisson standard errors

I have this question to answer for a class and am completely stumped. "The GLM log link and a dummy variable for gender (1=male, 0=female) has gender estimate 0.308. The SE is 0.038 assuming a ...
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1answer
182 views

Negative Binomial Regression: is parameter theta (R) the reciprocal of parameter kappa (SAS)?

After some frantic googling I do believe the answer is yes, but more so I am frustrated that the relation between the two parameters seems to be nowhere described explicitely so I do it here. (I hope ...
4
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1answer
259 views

Understanding over-dispersion as it relates to the Poisson and the Neg. Binomial

I am developing a Poisson-family glm model in R for a dataset that I have. This dataset has 650 entries with two measures of exposure. The model, though not that relevant to the question, is: ...
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2answers
627 views

When do Poisson and negative binomial regressions fit the same coefficients?

I’ve noticed that in R, Poisson and negative binomial (NB) regressions always seem to fit the same coefficients for categorical, but not continuous, predictors. For example, here's a regression with ...
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76 views

Herbivore density and group density modelling: Poisson GLM that overfits the data, or higher ranked negative binomial model that underfits the data?

I am an ecologist that has counted 11 different species of herbivores in about 110 blocks of two habitat types over 18 months, and I am interested in predicting the density across the study area from ...
6
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2answers
389 views

dispersion in summary.glm()

I conducted a glm.nb by glm1<-glm.nb(x~factor(group)) with group being a categorial and x being a metrical variable. When I try to get the summary of the ...
23
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2answers
1k views

Diagnostic plots for count regression

What diagnostic plots (and perhaps formal tests) do you find most informative for regressions where the outcome is a count variable? I'm especially interested in Poisson and negative binomial models, ...
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48 views

How to fit data to negative binomial

Ok, so I've looked at several of the already posted questions, but still am not quite certain how to go about this. My data looks like this: ...
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116 views

Analysis of negative binomial distributions using glm.nb() in R

I have observations of four different groups of people. The dependent variable are count data (medical emergencies in the past 2 months). For each group, the dependent variable follows a negative ...
2
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1answer
169 views

Negative binomial - likelihood ratio and likelihood ratio chi-squared

I ran a hierarchical negative binomial regression analysis, and got information relative to the log likelihood and likelihood ratio chi-squared in the output. I have the following questions regarding ...
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1answer
122 views

Calculate pseudo-$R^2$ from R's zero-inflated negative binomial regression

I'm looking into calculating a Pseudo $R^2$ used McFadden's method for a zero-inflated negative binomial regression. I'm unclear how to go about evaluating $\hat L(M_{intercept})$ in R. Any ...
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785 views

Model for underdispersed count data?

I am trying to model count data in R that is apparently underdispersed (Dispersion Parameter ~ .40). This is probably why a glm with family = poisson or a negative binomial (glm.nb) model are not ...
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2answers
742 views

Where does the offset go in Poisson/negative binomial regression?

(First of all, just to confirm, an offset variable functions basically the same way in Poisson and negative binomial regression, right?) Reading about the use of an offset variable, it seems to me ...
3
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1answer
196 views

Comparison negative binomial model and quasi-Poisson

I have run negative binomial and quasi-Poisson models based on an hypothesis testing approach. My final models using both methods have different covariates and interactions. It seems that there are no ...