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

[Nick Cox <njcoxstata@gmail.com>]

I don't want to repeat previous comments, but you introduce a new issue here

In essence, independence is everywhere assumed in statistics unless it
is explicit that there is dependence. The models discussed in this
thread _all_ are based on an assumption of independence. If you have a
serious issue of dependence that has to be modelled explicitly. There
is no sense in which the assumption of independence is special to
Poisson and somehow not made or not so important in other models. What
may be at fault here are many introductory or intermediate treatments
that fail to spell out that independence is assumed whenever it is.

You can't just say credibly that a counted distribution that is 0 up
"follows a normal distribution". At most such a distribution may be
roughly symmetric about its mean, which _in some circumstances_ might
be the most important detail. (It's how means behave which is the most
important issue determining whether many models might be useful.) But
the qualifications are vitally important too.

Nick

On Mon, May 7, 2012 at 3:58 PM, Laura R. <laura.roh@googlemail.com> wrote:

> the distribution of the variable "number of experts" consulted is not
> "zero-inflated", but rather follows a normal distribution from 0 to 5.
>
> 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.
>
> 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. Some people in this thread gave the hint on -gllamm- and
> -ssm-. I will keep that in mind and find out more about these models.
>
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