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

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25 views

what is the meaning and purpose of modeling a data?

Background: I collected a whole years access logs of my website, counted visit frequency for every user, and the numbers of user at each unique frequency, I got a distribution: $n_w \tilde\ D_w(f_w ; ...
0
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13 views

Reference on interpretation of similar observed values and average adjusted predictions

I analyzed the association between a count dependent variable (DV) and a dummy independent variable (IV) (coded 0 and 1) ...
2
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0answers
13 views

Did the Eggenberger-Pólya (1923) paper derive the negative binomial distribution with real-valued parameter?

The negative binomial distribution can be derived in many ways, but two famous ones are due to Greenwood & Yule (1920) and Eggenberger & Pólya (1923). Greenwood & Yule assumed unobserved ...
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0answers
22 views

Count Panel Data Event Study

Can anyone suggest a lecture/paper/textbook that covers an event study (eg. exogenous policy change) using count time-series (or penal) data? Or alternatively, just a general guideline as to what ...
6
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0answers
100 views

Overdispersion and modeling alternatives in Poisson random effect models with offsets

I have run into a number of practical questions when modeling count data from experimental research using a within-subject experiment. I briefly describe the experiment, data, and what I have done so ...
1
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0answers
28 views

Simulating Negative Binomial Arrivals

I am building a simulation. I want to generate arrivals according to a negative binomial process. The data will show the minute of each "customer" arrival and look something like the following: ...
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0answers
15 views

Convergence of distributions implies convolution (with itself) converge?

If 2 distributions converge in the limit, then do their convolutions also converge? e.g. I can show that for the Geometric distribution with random variable $T$, the scaled version with parameter ...
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1answer
30 views

What is the relationship between theta and size in negative binomial distribution?

In negative binomial regression glm.nb(y~x), I got a parameter theta and two coefficients? And then I want to use dnbinom(x, size, prob, mu, log = FALSE) to calculate the predicted probability. can ...
0
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1answer
59 views

Interpreting negative binomial regression with log transformed independent variables

My independent variables were highly skewed, so to normalise the distribution they were log transformed. Also since there were zeros in the data, I've added + 1 to transform the variables. This is ...
0
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0answers
57 views

Negative Binomial Regression model; algorithm did not converge

I am using R to run some negative binomial regression models. For model 1 I have the number of network in-degrees as the dependent variable, and Twitter followers, friends and number of Twitter ...
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1answer
50 views

Compare poisson and negative binomial regression with LR test

My question is related to the question Compare negative binomial models. I have some difficulties understanding UCLA guide in http://www.ats.ucla.edu/stat/r/dae/nbreg.htm (I am using ...
3
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1answer
146 views

Zero-inflated negative binomial models: why not use two separate models?

Zero-inflated negative binomial models have two components: a count component (negative binomial regression part) and a zero component (logistic regression part). Why not just run two separate ...
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0answers
24 views

How to prove NegativeBinomial(r,p) converges to Gamma(r,1) as p->0

Let $X\sim NegBin(r,p)$ and $Y\sim Gamma(r,1)$. How can I prove that $pX \overset{dist}\to Y$ as $p\to 0$. Is this statement the same as $X\overset{dist}\to Gamma(r,1/p)$. Thanks.
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1answer
72 views

Negative Binomial Distribution R

This question was given in class and I was wondering how to do this in R: "Sixty percent of a large lot of old spark plugs are still usable, and they can be individually tested to determine this. Let ...
2
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2answers
48 views

What to call exponentiated coefficients from a Poisson/negative binomial regression of cross-sectional data

In epidemiology, exponentiated coefficients are often reported as odds ratios, relative risks/ incidence rate ratios or hazard ratios. In the analysis of cross-sectional data using Poisson/negative ...
0
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0answers
62 views

R gam() throws error: “Can't correct step size”

I am computing a GAM on a large set of data sets. Almost all of them work, just this one data set makes gam() throw an error. I paste a code that reproduces this error here: ...
3
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0answers
162 views

Theoretical justification of choice for confidence interval exact method for the success probability parameter of negative binomial variable?

I have a computer experiment that runs the Bernoulli series with unknown probability $p$ of success. The experiment terminates when $m$ failures are observed. So, the unknown parameter $p$ has the ...
0
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0answers
79 views

Relative variable importance for glm & glm.nb - Percentage of deviance explained

I'm currently trying to calculate variable importance for multiple GLMs. I've got both continous and count data response variables. The first I modeled with gaussian GLM, the second with negative ...
0
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0answers
32 views

How to make beta coefficients comparable?

My study design delivers both, count data and continous outcomes (e.g., numbers of taxa vs. an diversity index). As these variables are used as response variables, I have to use negative binomial glm ...
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1answer
55 views

Why does the null deviance in glm.nb differ between models of the same response variable?

I'm struggeling to understand the topic of deviance. Let's have two models as follows: ...
0
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0answers
23 views

Negative binomial instead of ordinal logistic?

I have data with one metric and a discrete outcome that I'm trying to estimate the probability of. The outcome is a count, but it's a safe assumption that the increments aren't i.i.d. I thought an ...
2
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0answers
79 views

“weight” input in glm.nb function in R. How exactly does the weight affect the likelihood?

I would like to understand how the weight argument of glm.nb is affecting the likelihood function. I understand that glm.nb find the MLE in an alternating iteration process where for a given theta the ...
2
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0answers
25 views

Is there a simple model that assumes a negative relationship between the mean and variance of response?

Poisson and Negative Binomial models assume that the variance of response is greater or equal to the mean of response. Is there a simple model where that assumption is reversed, i.e. variance goes ...
0
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0answers
29 views

A/B testing zero inflated data

I am trying to conduct an A/B(/C) test to compare the performance of 3 different website pages but I'm facing issues regarding zero inflated data. I have data for each page regarding ...
8
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1answer
171 views

Low sample size: LR vs F - test

Some of you might have read this nice paper: O’Hara RB, Kotze DJ (2010) Do not log-transform count data. Methods in Ecology and Evolution 1:118–122. klick. Currently I am comparing negative binomial ...
3
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2answers
49 views

Poisson as a limiting case of negative binomial

I was reading "Maximum Likelihood Estimation for the Negative Binomial Dispersion Parameter" by Walter W. Pieogorsch, and in the intro it says the Poisson distribution is a limiting case of negative ...
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0answers
107 views

Count data in a Structural Equation Model

I am currently trying to fit a structural equation model (SEM) on a certain dataset using R (lavaan package). Some of the most important variables in my model are count data (abundance of different ...
0
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1answer
17 views

Why addition of discrete probability values for negative binomial does not match to the cumulative probability value, when it matches in Poisson?

When I manually calculate just negative binomial probability it matches to the value from Excel, or R. formula : (nCr) * (p^k) * ( q^(x-k) ) x = 1000 ; k = 4 ; p = 0.01 ; [ and n = x-1 ; r = ...
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33 views

How to interpret logarithmically transformed coefficients in negative binomial regression?

How can I interpret log-transformed independent variables in terms of percent change in a negative binomial regression?
8
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1answer
63 views

Is the negative binomial not expressible as in the exponential family if there are 2 unknowns?

I had a homework assignment to express the negative binomial distribution as an exponential family of distributions given that the dispersion parameter was a known constant. This was fairly easy, but ...
2
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1answer
94 views

When to use zero-inflated poisson regression and negative binomial distribution

I have a fairly simple dataset looking at the relationship between the first nesting date of a bird in a given year (Date) and the birds overall fledgling production from that year (Fledge; count data ...
3
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0answers
52 views

Interpretation of log transformed predictor in negative binomial regression

I mainly want to make sure that I'm making the correct interpretation here. I built a negative binomial regression model predicting a count variable. There was evidence of overdispersion or I would ...
2
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1answer
104 views

Quantiles of a compound gamma/negative binomial distribution

Are there any formulae for the quantiles of a compound gamma/negative binomial distribution? That is, suppose we have $$N \sim \text{NegBin}(\alpha, \lambda)$$ and conditional on $N$, $$Y = ...
0
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1answer
172 views

Interpretation of $\theta$ in negative binomial regression

First off, a very similar question has been asked before. But the answers to this question did not explain what high/low values of theta mean. Here's my crack at trying to figure out what high/low ...
1
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1answer
46 views

Zero-inflated negative binomial model for true zeros

The zeroinfl function in the pscl package in R assumes that zeros include both false zeros and true zeros. I have a zero ...
9
votes
1answer
142 views

Increased Type I error - GLM

Some of you might have read this nice paper: O’Hara RB, Kotze DJ (2010) Do not log-transform count data. Methods in Ecology and Evolution 1:118–122. klick. In my field of research (ecotoxicology) ...
4
votes
1answer
112 views

Generate pseudo-random overdispersed Poisson numbers

I have multiple sets of data which conform to overdispersed Poisson distributions which I can model with the alternative parameterization of a negative binomial distribution ($\mu$ and $D$ instead of ...
3
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1answer
86 views

GLM regression - help choosing model specification

I think I need to use a Poisson-family regression or negative binomial regression. My variables are as follows: Y is an integer value ranging from 0 to ~1200. It represents sums (number of species ...
0
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1answer
71 views

Validating residual plot count data (different levels)

I am studying the distribution of a marine species using the number of sightings as a dependent variable. When I am trying to validate the plots of the best model I am getting a non-usual pattern, and ...
3
votes
1answer
60 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
32 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
40 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
237 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
76 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 ...
4
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1answer
75 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
76 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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1answer
207 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
163 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
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0answers
25 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
109 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 ...