A discrete distribution defined on the non-negative integers that has the property that the mean is equal to the variance.

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Poisson regression with different exposures dependent and predictor variables

I am trying to fit a Poisson regession in R, using rates: $\ln(\mathrm{rate}_i) ~= a + bx_i + c \ln(\mathrm{old\_rate})_i$ My issue is that the predictor variable $(\mathrm{old\_rate})$ is also a ...
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16 views

Idiosyncratic error term in fixed effects Poisson

Cameron and Trivedi (2013: 346) and Wooldridge (2010) suggest fixed-effects Poisson with multiplicative heterogeneity.E[y_it│x_it,α_i ]=α_i exp⁡(x_it'β), where α_i is the unobserved heterogeneity. If ...
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1answer
18 views

Poisson regression with offset vs logistic regression

I am thinking to use Poisson regression with an offset variable instead of a logistic regression in case where event is rare, since p (probability of success) is very small and n (sample size is ...
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12 views

DIfferent zero-inflated poisson model outputs of Frequentist and Bayesian

I modeled zero-inflated poisson regression using crime data. There are 10034 obs and let assume spatial autocorrelation is not significant. For the Frequentist approach, R was used and code is ...
2
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0answers
16 views

How to determine counts of viruses from limiting dilution assay

My question relates to a common experiment in the field of virology. Let me give some background so you understand why I'm asking this question. When producing virus for an experiment you typically ...
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15 views

Number of Exponential Summands in fixed interval is Poisson

What is the most clever way to prove that the number of independent exponential summands in a fixed interval is distributed as a Poisson random variable? I can do it one way, but I would like to know ...
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24 views

Generating Poisson random Variable [on hold]

Please help me in correcting the following code for generating 3 Possion random variables. n=3 lambda=.7 p=exp(-lambda) f=p set.seed(34231) x <-0 for(i in 1:n) { U=runif(1) show (p) show (f) ...
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10 views

Estimating the uncertainty in the peak of a non-stationary poisson process

I have daily counts of observed disease cases for a single location. I am interested in the peak timing of the outbreak of the disease and want to assess the uncertainty in the peak estimate. In other ...
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1answer
32 views

What is the difference between Poisson Regression and Log-linear Models in terms of their usage and which should I use?

I'm currently analyzing a data set from an experiment, where participants could give one of three types of answers: 1) Correct, 2) incorrect-congruent, 3) incorrect-incongruent. The priming ...
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18 views

Distinguishing between Poisson distribution and a similar distribution w/ small mean

I have an experiment where if all is going well the measured distribution should be Poisson (to very good approximation) with mean $\lambda \sim .1$, but if something goes wrong the distribution will ...
3
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1answer
62 views

log ratio of Poisson means versus logit of binomial probability

Assume that two observed counts C1 and C2 are independent realizations of two Poisson processes: ...
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22 views

Expectation of y given u when it follows Poisson distribution

So I was reading Generalized Linear Models with Random Effects by Youngjo Lee, in chapter 6 about Hierarchical GLMs there's this example: Suppose $y|u$ is Poisson with mean $\mu = E(y|u) = ...
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11 views

how to interpret interaction in Poisson regression using SAS

I tried to run Poisson regression models using SAS by including interaction terms and offset by log population. All dependent variables were categorical. In the first model, I tested the interaction ...
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27 views

Poisson regression on Lung Cancer

I am a statistic student and I'm trying to study the effects of smoking on lung cancer rates. Below you will find what I did. My question is about the homoskedasticity, I think that the assumpion is ...
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25 views

Zero-truncated Poisson model

In the theory of generalised linear models, you may use the exponential family to find the mean and variance of certain distributions. How would the mean and expectation of the zero-truncated Poisson ...
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13 views

Poisson regression residual analysis

In a three factor poisson (log-linear) model $(A*B*C)$, when the highest interaction term $(A:B:C)$ is dropped, the response/raw residuals are exactly the same for different levels of two of the ...
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21 views

Find mean of Poisson process between two known options

I think my question is simple, but somehow it's ruining my day. My problem is: I observe a Poisson process, and I want to find out which, between two known options, mean_1 or mean_2, is the true ...
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2answers
83 views

Why two 'modes' for a Poisson Distribution with $\lambda$ an integer?

Let $X\sim \operatorname{Poi}[\lambda]$ such that $\lambda\in\mathbb{N}$. ...
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13 views

Confidence interval for fitted lambda from Possion distrubtion

So my question is: you are given a set of data and you know the distribution is Possion with parameter lamda > 0. I figure out xbar is 4.06, and the z value we are using is 1.96 and n=50? But how can ...
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1answer
33 views

offset in glm for poisson regression

The offset argument in the glm() quite troubles me. As below, m3 is the usage of offset that I have seen. m4 is a manually calculated analog. But the result obtained is completely different, with m3 ...
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1answer
49 views

Log-linear model, Poisson regression, categorical variable with 100 levels

I want to compare the incidence rate(asum) of 100 different cities(cityID) to see if there are significant differences among them. Given that the incidence rate is following Poisson, so it is a ...
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48 views

If the # of people in a room is Poisson distributed, and you observe someone enter, what's the distribution of the # of people?

I hope this question is properly formulated. It's just something that occurred to me spontaneously. Consider a random variable $X$ representing some count data -- for instance, the number of people ...
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2 views

What component of the result should I look at when doing a LLM model fit?

I am running mixed effects models with poisson and negative binomial fits. To asses which of the models are better, what components of the models should I look at? Some popular methods I follow: a) ...
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10 views

Wald, LR and LM tests for Poisson distribution

Assume that $y$ is random variable which distributes: $$f(y)=\frac{e^{-\lambda}\lambda^{y}}{y!} $$ Where $\lambda=e^{\alpha+X\beta}$ and $\alpha$ and $\beta$ are unknown parameters and we assume that ...
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1answer
18 views

Generalized poisson model with time parameter

I tried finding this on the internet, but with little success. How do I get a generalized expression involving rate parameter and time parameter for the Poisson process? The expression, $P(n) = ...
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8 views

Estimated values for Chi-square

To test if my point pattern is random, I am going to conduct a Chi square test. The data has 40 points divided to 3 by 3 tiles. Should I use Binomial or Poisson probability to calculate expected ...
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11 views

Can I use an offset for the maximum number of consecutive trades in an experimental market?

I have run a study where we let students interact as buyers and sellers in an experimental markt. Every period buyers can buy from one single seller and sellers can only sell to one single buyer. We ...
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14 views

Systematic component variation

The appendix of the paper of McPherson et al (1982) contains a derivation of the systematic component variation SCV. I understand the derivation with exception of the first step. Here are the ...
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1answer
134 views

Question on Poisson Distribution (Assignment Help)

I've been given the following question which was part of a past exam paper. Q3) Trains arrive at a station at the rate of 25 per hour. a) What is the probability that the time between trains ...
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1answer
55 views

Poisson Regression in R based on categorical time variables

I am trying to make a prediction on the number of visitors of a website and am wondering if it can be done based only on categorical time variables. I received some guidance on how to structure my ...
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22 views

Standardized residuals vs fitted values for Poisson regression

McCullagh and Nelder's book on glm suggest to plot standardized deviance residuals against either the linear predictor ($\hat{\eta}$) or the fitted values ($\hat{\mu}$) transformed to the constant ...
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24 views

Count data that can take only 4 values

What is a good model for estimating a regression whose count dependent variable that only has 4 values: 0, 1, 2, 3? The variable is not truncated, it is just something that can only be from 0-3. I've ...
0
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1answer
57 views

Standard Error differences Binomial Regression vs Poisson Regression

I'm running three different models on a dataset found in table 9.1 of Dobson's Introduction to Generalized Linear Models textbook. Model 1 is a poisson regression, Model 2 is a binomial regression ...
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19 views

Offset instead of percent data?

In R I want to build a GLM explaining the fraction of a coral perimeter that is covered by different algae. I measured the perimeter of the coral (in cm, integer values) and fraction that is contacted ...
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1answer
32 views

Linear Mixed Effects Model [closed]

I have data with some of the following columns: Site (categorical, 1-4), Species (Categorical, 1-21), Damage (continuous), and Age (categorical, 0-6). Age represents the visits to each site where I ...
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3 views

Validation of prediction interval for count data

I have developed a random-effects (frailty) survival model for repeated events which enables calculating individual-specific mean and prediction interval for the cumulative incidence (rate) of future ...
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0answers
10 views

What is the best test to measure deviations from tiny proportions?

What is the best (most reliable and robust) test to measure deviations from tiny expected proportions (e.g., p0 < 10^-6) in a huge sample? Binomial? Poisson? Negative binomial? Something else? ...
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1answer
33 views

Why is the Negative Binomial typically preferred over the Poisson?

I know that the Poisson is a special type of negative binomial, but from some shallow readings I've noticed that people claim that the Negative Binomial is better than the Poisson as it accounts for ...
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1answer
37 views

Poisson Convergence Example

For any $n\ge1,$ let $X_{n1},...,X_{nn}$ be independent with $$P\{X_{nk}=5\}=1-P\{X_{nk}=0\}=p_{nk}, \ k=1,...,n$$. Assume that $$\lim_{n\rightarrow \infty} \max_{1\le k \le n} p_{nk}=0$$ and ...
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23 views

Need help interpreting lmer output (ie should glm and lmer p values differ significantly?) [duplicate]

I posted this in Stack Exchange, but figure it may be better suited here given that it isn't a programming question per se: I initially ran a mixed model to calculate p values from a mixed model: ...
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1answer
44 views

Need help interpreting lmer output

I'm not sure whether this belongs here (or Cross Validated), but until somebody tells me otherwise, I'll keep it here. I initially ran a mixed model to calculate p values from a mixed model: ...
2
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1answer
29 views

Unbiased estimators of a transformed Poisson

So the question I have is$:$ Let $X$ follow a Poisson distribution with mean $\mu$, except that $X=0$ cannot be observed; this gives a random variable $Y$ which has a truncated Poisson ...
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17 views

Which statistical test is most appropriate for my count data?

I did a study looking at how the number of times a specific behaviour is performed during a courtship ritual is affected by temperature treatment, while trying to control for the body size of the male ...
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1answer
73 views

Forecasting Poisson, accuracy and prediction intervals

I'm trying to forecast Poisson data, divided in groups, of 1-26 months of data, depending on the group. Of the pooled data ...
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30 views

Is Quasi-Poisson the same thing as fitting a Poisson GEE model?

The title says it all. I'm wondering if someone can help me understand the difference (if there even is one) between a Quasi-Poisson model and fitting a Poisson Regression Model using GEE? It is my ...
2
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1answer
18 views

What method for forecasting error measuring in a poisson process?

There's so much different measures for the forecast error that I kind of lose the sight on which one to use. Out of the following: MAPE, ...
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14 views

Is there a goodness of fit test for Poisson regression with complex survey data?

I am doing an analysis of complex survey data using a binary response variable and several covariates. I am using Poisson with robust standard errors to obtain relative risks. Is there an ...
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25 views

How to calculate MSPE in winbugs when I use Zero Inflated Poisson regression?

I have had question about Winbugs code. I used ZIP(Zero Inflated Poisson) regression code in winbugs, and I want to compare two models(Poisson Model and ZIP model) using MSPE(Mean Square Predict ...
0
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1answer
51 views

Estimate the number of points scored by a team in baseball

Let’s say I’d like to estimate the number of runs Team A will score against Team B Team A (away) vs Team B (home). Starting pitcher for Team B is a lefty named “Ben James” Team A scores 5.2 runs per ...
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46 views

UMVUE for $E(y^2)$ in Poisson distribution

If $Y \sim \text{Poisson}(\lambda)$. How do I find the UMVUE for $E(y^2)$? I know that $E(y^2)$ is $\lambda$+$\lambda^2$, since I want to use Rao-blackwell thereom, I need a complete sufficient ...