Contents
What is quasi-Poisson model?
The Quasi-Poisson Regression is a generalization of the Poisson regression and is used when modeling an overdispersed count variable. The Poisson model assumes that the variance is equal to the mean, which is not always a fair assumption.
How do you test for zero-inflation?
Details. If the amount of observed zeros is larger than the amount of predicted zeros, the model is underfitting zeros, which indicates a zero-inflation in the data. In such cases, it is recommended to use negative binomial or zero-inflated models.
What is meant by overdispersion?
In statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model. Conversely, underdispersion means that there was less variation in the data than predicted.
How does Dharma work and what does overdispersion mean?
DHARMa works by simulating new data from the fitted model, and then comparing the observed data to those simulated (see DHARMa’s nice vignette for an introduction to the idea). Overdispersion means the assumptions of the model are not met, hence we cannot trust its output (e.g. our beloved $P$-values)!
When does overdispersion occur in a Poisson distribution?
Such data would be overdispersed for a Poisson distribution. Also, overdispersion arises “naturally” if important predictors are missing or functionally misspecified (e.g. linear instead of non-linear).
Is the negative binomial a good upgrade for Poisson?
For Poisson, the most obvious “upgrade” is the negative binomial, which includes in fact a dispersion parameter similar to $ au$ above. Already here we see that the ratio of deviance and df is near $1$ and hence probably fine.
Why does the zero inflation test have negative overdispersion?
This may be due to a misspecified model (e.g. missing important predictors), leading to underfitting of the high values (all large values have high quantiles, indicating that these residuals (O-E) are all positive and large). The overdispersion, and just for fun also the zero-inflation test, are negative.