Re: st: zero-inflated analyses: when do you decide that is zero-inflated?

[David Hoaglin <dchoaglin@gmail.com>]

Dear Cris.

I don't think that outcome variable is a candidate for being Poisson
or negative binomial, either zero-inflated or not.  Both the Poisson
distributions and the negative binomial distributions assign positive
probability to all nonnegative values, not just 0 through 4.  Both of
those families of distributions have truncated versions, but the
process underlying your data doesn't look like it involves truncation.

Your outcome variable is a legitimate numerical variable, but people
sometimes use an ordinal logit model for such data when the number of
values is small.

Would it be appropriate to look at the association(s) among the
positives on the 4 tests?  If positive reactions to the 4 allergens
were unrelated (i.e., independent), you could predict the numbers of
positives on the 4 from the marginal probabilities of a positive
reaction to the individual allergens.  It may be instructive to list
the 16 possible combinations and their frequencies in your data.

David Hoaglin

On Mon, Jul 15, 2013 at 10:49 AM, Cris Dogaru (Oregon State
University) <statamplus@gmail.com> wrote:
> Dear Stata users,
>
> I couldn't find an answer to this apparently simple question: how does
> one decide that a distribution is zero-inflated, so that one can use
> zero-inflated Poisson regression or zero-inflated negative binomial
> regression?
>
> More concrete: my outcome variable is number of positive skin prick
> tests (done for 4 allergens, therefore the number has a range 0 to 4).
> Here are the summary tables; is this zero-inflated?..
>
>
> spt_number -- number of positive (wheal>3mm) STP
> -----------------------------------------------------------
>               |      Freq.    Percent      Valid       Cum.
> --------------+--------------------------------------------
> Valid   0     |        853      57.02      58.30      58.30
>           1     |        286      19.12      19.55      77.85
>           2     |        176      11.76      12.03      89.88
>           3     |        105       7.02       7.18      97.06
>           4     |         43        2.87       2.94     100.00
>          Total |       1463      97.79     100.00
> Missing .     |         33       2.21
> Total         |       1496     100.00
> -----------------------------------------------------------
>
> . fsum spt_number
>
>    Variable |        N     Mean       SD      Min      Max
> ------------+---------------------------------------------
>  spt_number |     1463     0.77     1.10     0.00     4.00
>
> Many thanks
> Cristian Dogaru
> ISPM, University of Bern
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