Re: st: which -cmp- option to use for poisson model with count data?

[Maarten Buis <maartenlbuis@gmail.com>]

On Mon, May 7, 2012 at 4:58 PM, Laura R. wrote:
> the distribution of the variable "number of experts" consulted is not
> "zero-inflated", but rather follows a normal distribution from 0 to 5.

That is very implausibly, if not impossible (assuming that with
"normal distribution" you mean the Gaussian distribution that is often
called "bell shaped" in introductory statistics books).

> As there theoretically can be more than 5 experts, Nick sais, if I
> understand correctly, that this would be a hint to use Poisson model,
> as I would have to label the highest "category" "5 or more" in ordered
> probit.

Neither Poisson nor ordered probit/logit care (and thus ignore) how
you label values, so your summary of Nick's reasoning is not true.
Based on the information you have given us I would lean towards
Poisson, but to make this kind of choice you really need to have
detailed knowledge of the data, the exact question that was asked and
the possible answer categories (don't trust the variable label, look
in the codebook and the original questionnaire), the process that is
being measured, etc. etc.

> However, I have read that the events have to be independent of each
> other in the Poisson model, e.g. emergency room admission (taking
> David Roodman's example). This would be a reason for not using
> Poisson. E.g., deciding on getting a third child probably depends on
> how life is with 2 children --> ordered probit model. COnsulting
> another expert can also depend on what the last one had said.
>
> I think I will try the ordered probit model again, as this can be used
> within -cmp-, while the Poisson model cannot. If the parallel
> regression assumption or other assumptions for ordered probit models
> turn out to be violated, I will try the Poisson model, but then I have
> to come up with an idea similar to -cmp- that can be used with
> Poisson.

I think that that is a bad idea. If you think that the violation of
the independence assumption is important enough to reject the Poisson
model, than you should derive how this plays out in the ordered probit
model. I would not be surprised if that model also implies
independence or extremely restricted constraints on the dependence:
how else can it summarize the effect of a variable with only one
parameter? In general, focusing on just one assumption is usually a
very bad way of choosing between models.

-- Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany


http://www.maartenbuis.nl
--------------------------
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