# [R] Poisson Regression: questions about tests of assumptions

Wensui Liu liuwensui at gmail.com
Mon Oct 15 00:38:05 CEST 2012

```just a side note for your 4th question.

for a small sample, clarke test instead of vuong test might be more
appropriate and the calculation is so simple that even excel can
handle it :-)

On Sun, Oct 14, 2012 at 12:00 PM, Eiko Fried <torvon at gmail.com> wrote:
> 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
>
>         [[alternative HTML version deleted]]
>
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> and provide commented, minimal, self-contained, reproducible code.

--
==============================
WenSui Liu
Credit Risk Manager, 53 Bancorp
wensui.liu at 53.com
513-295-4370

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