I would like to test in R 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.

1) 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?

2) 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 anova(m1,m2)?

3) 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?

4) 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?

5) ats.ucla.edu 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 if. I had expected the regression to be
the same and just use a different family.

Thank you
T

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