RE: st: RE: AW: Sample selection models under zero-truncated negative binomial models

 From "Lachenbruch, Peter" To Subject RE: st: RE: AW: Sample selection models under zero-truncated negative binomial models Date Fri, 5 Jun 2009 09:28:27 -0700

```I think the situations may be distinct:  having no hospital visits seems different from having one or more.  If these are not part of a mixture distribution (i.e., 0 visits is identifiable) one can estimate the probability of a person having 0 visits and then the count of number of non-zero visits.  If not identifiable, one can use zero-inflated Poisson or zero-inflated negative binomial.

The problem seems to separate naturally into the two parts. If you want a mean number of visits you can get it, but I'm unsure of the interpretation since there's a fraction that don't have any visits that is greater than that expected under the Poisson model.  In one dissertation, a student had 95% zeros and the rest were positive.  The idea was to predict costs of hospitalization - this had big implications for insurance companies.  In this case, the likelihood of finding hospitalization in a household survey may also have a preponderance of zeros.

Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols
Sent: Friday, June 05, 2009 9:15 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: AW: Sample selection models under zero-truncated negative binomial models

John Ataguba <johnataguba@yahoo.co.uk> :

Again, why split the analysis?  If you are interested in the count,
use a count model, and then talk about what the results from that
model predict about the probability of a nonzero count when you are
interested in whether people have any visits.  You don't seem to have
any theory requiring "standard logit/probit model" assumptions.
-poisson- seems the natural starting point.

Why would you drop the zeros when trying to assess how many GP visits
a person seems likely to make conditional on X?  Zero is one possible
outcome...

On Fri, Jun 5, 2009 at 10:03 AM, John Ataguba <johnataguba@yahoo.co.uk> wrote:
> Hi Austin,
>
> Specifically, I am not looking at the time dimension of the visits.  The data set is such that I have total number of visits to a GP (General Practitioner) in the past one month collected from a national survey of individuals.  Given that this is a household survey, there are zero visits for some individuals.
>
> One of my objective is to determine the factors that predict positive utilization of GPs.  This is easily implemented using a standard logit/probit model.  The other part is the factors that affect the number of visits to a GP.  Given that the dependent variable is a count variable, the likely candidates are count regression models.  My fear is with how to deal with unobserved heterogeneity and sample selection issues if I limit my analysis to the non-zero visits.  If I use the standard two-part or hurdle model, I do not know if this will account for sample selection in the fashion of Heckman procedure.
>
> I think the class of mixture models (fmm) will be an anternative that I want to explore. I don't know much about them but will be happy to have some brighter ideas.
>
> Regards
>
> Jon
>
>
> ----- Original Message ----
> From: Austin Nichols <austinnichols@gmail.com>
> To: statalist@hsphsun2.harvard.edu
> Sent: Friday, 5 June, 2009 14:27:20
> Subject: Re: st: RE: AW: Sample selection models under zero-truncated negative binomial models
>
> Steven--I like this approach in general, but from the original post,
> it's not clear that data on the timing of first visit or even time at
> risk is on the data--perhaps the poster can clarify?  Also, would you
> propose using the predicted hazard in the period of first visit as
> some kind of selection correction?  The outcome is visits divided by
> time at risk for subsequent visits in your setup, so represents a
> fractional outcome (constrained to lie between zero and one) in
> theory, though only the zero limit is likely to bind, which makes it
> tricky to implement, I would guess--if you are worried about the
> nonnormal error distribution and the selection b
>
> Ignoring the possibility of detailed data on times of utilization, why
> can't you just run a standard count model on number of visits and use
> that to predict probability of at least one visit?  One visit in 10
> years is not that different from no visits in 10 years, yeah?  It
> makes no sense to me to predict utilization only for those who have
> using the whole sample, including the zeros.  I.e. run a -poisson- to
> start with.  If you have a lot of zeros, that can just arise from the
> fact that a lot of people have predicted number of visits in the .01
> range and number of visits has to be an integer.  Zero inflation or
> overdispersion also can arise often from not having the right
> specification for the explanatory variables...  but you can also move
> to another model in the -glm- or -nbreg- family.
>
> On Tue, Jun 2, 2009 at 1:21 PM, <sjsamuels@gmail.com> wrote:
>> A potential problem with Jon's original approach is that the use of
>> services is an event with a time dimension--time to first use of
>> services.  People might not use services until they need them.
>> Instead of a logit model (my preference also),   a survival model for
>> the first part might be appropriate.
>>
>> With later first-use, the time available for later visits is reduced,
>> and  number of visits might be associated with the time from first use
>> to the end of observation.  Moreover, people with later first-visits
>> (or none) might differ in their degree of  need for subsequent visits.
>>
>> To account for unequal follow-up times,  I suggest a supplementary
>> analysis in which the outcome for the second part of the hurdle model
>> is not the number of visits, but the rate of visits (per unit time at
>> risk).
>>
>> -Steve.
>>
>> On Tue, Jun 2, 2009 at 12:22 PM, Lachenbruch, Peter
>> <Peter..Lachenbruch@oregonstate.edu> wrote:
>>> This could also be handled by a two-part or hurdle model.  The 0 vs. non-zero model is given by a probit or logit (my preference) model.  The non-zeros are modeled by the count data or OLS or what have you.  The results can be combined since the likelihood separates (the zero values are identifiable - no visits vs number of visits).
>>>
>>>
>>> -----Original Message-----
>>> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Martin Weiss
>>> Sent: Tuesday, June 02, 2009 7:02 AM
>>> To: statalist@hsphsun2.harvard.edu
>>> Subject: st: AW: Sample selection models under zero-truncated negative binomial models
>>>
>>> *************
>>> ssc d cmp
>>> *************
>>> -----Ursprüngliche Nachricht-----
>>> Von: owner-statalist@hsphsun2.harvard.edu
>>> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von John Ataguba
>>> Gesendet: Dienstag, 2. Juni 2009 16:00
>>> An: Statalist statalist mailing
>>> Betreff: st: Sample selection models under zero-truncated negative binomial
>>> models
>>>
>>> Dear colleagues,
>>>
>>> I want to enquire if it is possible to perform a ztnb (zero-truncated
>>> negative binomial) model on a dataset that has the zeros observed in a
>>> fashion similar to the heckman sample selection model.
>>>
>>> Specifically, I have a binary variable on use/non use of outpatient health
>>> services and I fitted a standard probit/logit model to observe the factors
>>> that predict the probaility of use..  Subsequently, I want to explain the
>>> factors the influence the amount of visits to the health facililities. Since
>>> this is a count data, I cannot fit the standard Heckman model using the
>>> standard two-part procedure in stata command -heckman-.
>>>
>>> My fear now is that my sample of users will be biased if I fit a ztnb model
>>> on only the users given that i have information on the non-users which I
>>> used to run the initial probit/logit estimation.
>>>
>>> Is it possible to generate the inverse of mills' ratio from the probit model
>>> and include this in the ztnb model? will this be consistent? etc...
>>>
>>> Are there any smarter suggestions?  Any reference that has used the similar
>>> sample selection form will be appreciated.
>>>
>>> Regards
>>>
>>> Jon

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