28
votes
Accepted
How to deal with overdispersion in Poisson regression: quasi-likelihood, negative binomial GLM, or subject-level random effect?
Poisson regression is just a GLM:
People often speak of the parametric rationale for applying Poisson regression. In fact, Poisson regression is just a GLM. That means Poisson regression is justified ...
- 64.1k
27
votes
Is it possible that the AIC and BIC give totally different model selections?
It is possible indeed. As explained at https://methodology.psu.edu/AIC-vs-BIC, "BIC penalizes model complexity more heavily. The only way they should disagree is when AIC chooses a larger model than ...
- 20.7k
20
votes
Diagnostic plots for count regression
This is an old question, but I thought it would be useful to add that my DHARMa R package (available from CRAN, see here) now provides standardized residuals for GLMs and GLMMs, based on a simulation ...
- 8,409
16
votes
Accepted
Interpreting Poisson regression coefficients
Let's say you were hired last year by a firm on a starting salary of 100,000 dollars. After one year of excellent performance on the job, you receive a raise and your new salary is 120,000 dollars. ...
- 20.7k
16
votes
Accepted
Are over-dispersion tests in GLMs actually *useful*?
In principle, I actually agree that 99% of the time, it's better to just use the more flexible model. With that said, here are two and a half arguments for why you might not.
(1) Less flexible means ...
- 21.4k
15
votes
Accepted
Log-likelihood function in Poisson Regression
In Poisson regression, there are two Deviances.
The Null Deviance shows how well the response variable is predicted by a model that includes only the intercept (grand mean).
And the Residual Deviance ...
- 4,796
14
votes
Are over-dispersion tests in GLMs actually *useful*?
Although this is my own question, I'm also going to post my own two-cents as an answer, so that we add to the number of perspectives on this question. The issue here is whether or not it is sensible ...
- 130k
14
votes
Accepted
Poisson regression appropriate?
Poisson regression does not appear to be appropriate in your case.
First off, Poisson regression models counts, and your events are binary, so if at all, logistic regression would be more appropriate....
- 129k
13
votes
Is it possible that the AIC and BIC give totally different model selections?
Short answer: yes, it is very possible. The two apply different penalties based on the number of estimated parameters (2k for AIC vs ln(n) x k for BIC, where k is the number of estimated parameters ...
- 549
13
votes
Why is linear regression results so much different from Poisson regression?
The biggest difference there will be caused by the fact that the Poisson GLM by default will be using the log link while the regression model uses an identity link. That is, it will fit a model
$\...
- 287k
13
votes
Accepted
When is it appropriate to use a zero-inflated Poisson regression model?
A zero-inflated Poisson model (or any other zero-inflated model) is a special case of a mixture model, i.e., one where we model observations as coming from a mixture of two or more underlying and ...
- 129k
12
votes
Why are Poisson regression coefficients biased?
The default link function is the log function for Poisson, this means:
$$\mathbb{E}[y]=\exp\left(\log(5)+\log(x)\right)$$
If you specify your glm model as ...
- 25.1k
12
votes
Accepted
Poisson regression intercept downward bias when true intercepts are small
The score function is exactly unbiased
$$E_{\beta_0}[\sum_i x_i(y_i-\mu_i)]=0$$
In your case that simplifies to
$$E_{\beta_0}[\sum y_i-\exp\beta_0]=0$$
The parameter estimate is a non-linear function ...
- 43.3k
12
votes
Accepted
Why is there little difference in glm fit using poisson and gaussian family for Poisson data?
You’ve got models to two different data sets.
For the Poisson regression, your true conditional expected values (lambda values) are given by $\exp(0.43x+0.2)$.
For the linear regression, your true ...
- 65.6k
11
votes
Accepted
Poisson xgboost with exposure
According to the answer in:
https://stackoverflow.com/questions/34896004/xgboost-offset-exposure
xgboost can handle offset term ...
- 276
10
votes
Basic R-Squared in Poisson Regression
A Poisson regression is nonlinear. Yes, it’s called a generalized linear model, but it has a nonlinear link function. Poisson regression is not linear.
When a regression is nonlinear, the residuals ...
- 65.6k
10
votes
How do I combine predictions of four Poisson regressions that use the same independent variable?
Let's Think About Restrictions
If you want to the predictions of each quadrant to sum to the total, you have to incorporate that restriction into the model. Presently, there is nothing relating the 4 ...
- 38.5k
10
votes
What exactly needs to be independent in GLMs?
What is actually required is conditional independence of the response variable. Conditional on the regressors, that is. A Poisson regression model - for independent data - is no different from an ...
- 64.1k
10
votes
When is it appropriate to use a zero-inflated Poisson regression model?
Poisson regression sucks, but zero-inflating your models is fine
As previously discussed here,
here and here the Poisson regression is almost always a bad count model and is far inferior to the ...
- 130k
10
votes
Accepted
What is special about the Poisson/Binomial distributions such that they have special regression estimation techniques?
Poisson and Binomial are reasonable distributions for raw data values for a response variable: Y = integer counts and Y = binary yes/no answers are fairly common. There are also Beta regression (Y = ...
- 4,451
9
votes
Accepted
Poisson regression with strong pattern in residuals
I would not begin by transforming the response variable (DV).
I'd start by considering whether you have the right link function or whether you should transform some x's (independent variables).
If ...
- 287k
9
votes
Accepted
Poisson Regression : expectation vs probability for each outcome
If you have a fitted expectation (as you show you can get), using that as a parameter in a Poisson pdf should work.
That is, given $\hat{\lambda}_i = E(Y=0|X=\boldsymbol{x}_i)$ you can use that to ...
- 287k
9
votes
Accepted
The difference of Standard Error between glm(y~x, family=poisson(link=identity)) and optim() in R
In statistical likelihood theory, minus the second derivative of the log-likelihood function is called the observed information. We might write this as
$$
I = -\ddot \ell(y; \theta)
$$
where the dots ...
- 13.3k
9
votes
Accepted
Counting samples seem to not be Poisson distributed, need sanity check
A true Poisson distribution will have its mean exactly equal to its variance. For a sampling of a Poisson distribution, however, there will be some deviation - with only 20 samples, it's unlikely that ...
- 10.1k
9
votes
Accepted
What better I use for Negative Binomial Regression with library(MASS) glm(family=negative.binomial) or glm.nb?
The negative binomial model is a generalized linear model only when the overdispersion parameter theta is known. In applications, we don't know it, and it needs to be estimated along with the other ...
- 35.7k
9
votes
Accepted
Robust standard errors for a Poisson regression with/without an offset
How could they possibly be different?
The two sandwich estimators are estimators for different semiparametric models. The individual-observation one is for a model where observations are all ...
- 43.3k
9
votes
Accepted
Poisson regression with small denominators/counts
First of all, a binomial GLM is more appropriate than a Poisson GLM. (A Poisson GLM is used for unbounded counts; your counts are bounded by the total number of surgeries.) The counts aren't that ...
- 1,058
8
votes
Accepted
Can Weights and Offset lead to similar results in poisson regression?
(with your R code, you could replace "poisson" with "quasipoisson" to avoid all the warnings that get generated. Nothing else of import will change. See (*) below). Your reference use the term "...
- 81.6k
8
votes
Accepted
How does poisson regression handle zeros anyway?
The Poisson model is $$y = \exp \left(\alpha + \beta \cdot x + \varepsilon \right).$$
The way you get an outcome of zero is when the index $\alpha + \beta \cdot x + \varepsilon$ is large and negative....
- 37.8k
8
votes
Why are Poisson regression coefficients biased?
That isn't how poisson regression works. The link function for poisson regression is the log, so if you did something like
...
- 38.5k
Only top scored, non community-wiki answers of a minimum length are eligible