I would like to test in what regression fits my data best. My dependent variable is a count, and has a lot of zeros.
And I would need some help to determine what model and family to use (poisson or quasipoisson, or zero-inflated poisson regression), and how to test the assumptions.
- Poisson Regression: as far as I understand, the strong assumption is that dependent variable mean = variance. How do you test this? How close together do they have to be? Are unconditional or conditional mean and variance used for this? What do I do if this assumption does not hold?
- I read that if variance is greater than mean we have overdispersion, and a potential way to deal with this is including more independent variables, or family=quasipoisson. Does this distribution have any other requirements or assumptions? What test do I use to see whether (1) or (2) fits better - simply
- I also read that negative-binomial distribution can be used when overdispersion appears. How do I do this in R? What is the difference to quasipoisson?
Zero-inflated Poisson Regression: I read that using the vuong test checks what models fits better.
> vuong (model.poisson, model.zero.poisson)
Is that correct? What assumptions does a zero-inflated regression have?
UCLA's Academic Technology Services, Statistical Consulting Group has a section about zero-inflated Poisson Regressions, and test the zeroinflated model (a) against the standard poisson model (b):
> m.a <- zeroinfl(count ~ child + camper | persons, data = zinb)
> m.b <- glm(count ~ child + camper, family = poisson, data = zinb)
> vuong(m.a, m.b)
I don't understand what the
| persons part of the first model does, and why you can compare these models. I had expected the regression to be the same and just use a different family.