Re: st: "pooled" xtmepoisson with unconstrained error variance

[Rebecca Pope <rebecca.a.pope@gmail.com>]

Steve,
I've tried out the syntax in the Gutierrez slides. It does work (i.e.
Stata does not issue an error and the model converges) for
-xtmepoisson- in Stata 12, at least with the sample data sets.

For the curious, the use of heterogeneity in multilevel models is
discussed in more detail in Rabe-Hesketh and Skrondal (2012)
_Multilevel and Longitudinal Modeling Using Stata, Ed 3_. They only
discuss -xtmixed-, no examples with -xtmelogit-/-xtmepoisson-.
Nevertheless, the discussion is helpful and I would not have checked
out Vol I on continuous responses without your suggestion Steve, so
thanks!

Regards,
Rebecca
On Mon, Nov 26, 2012 at 8:36 AM, Rebecca Pope <rebecca.a.pope@gmail.com> wrote:
>
> Thanks Steve. I'll try it out and let you know.
>
> Best,
> Rebecca
>
>
> On Sun, Nov 25, 2012 at 5:35 PM, Steve Samuels <sjsamuels@gmail.com> wrote:
> >
> >
> > Bobby Gutierrez showed how to model unequal variances with -xtmixed- in
> > www.stata.com/meeting/fnasug08/gutierrez.pdf. I don't have time to try
> > this, but at first glance it looks like his trick for doing this (pp
> > 14-16) will work with -xtmelogit-.
> >
> > Steve
> >
> > On Nov 25, 2012, at 4:59 PM, Rebecca Pope wrote:
> >
> > Hello,
> > I need to estimate a Poisson model for two groups with unequal
> > variance where the data is comes from observations on patients over
> > time nested within clinics (i.e. level 1 is time (measurement
> > occasion), level 2 is the patient, and level 3 is the clinic). I am
> > using Stata 12.1. I think -xtmepoisson- is a natural choice for the
> > analysis, except that for the time being I'm stuck estimating separate
> > equations for each group.
> >
> > In the interest of fixing terms, by "pooled" I mean that I've taken a
> > separate equation for each group and written them as one "master"
> > equation.
> >
> > Bill Gould discusses something similar to my problem in the linear
> > regression context at:
> > http://www.stata.com/support/faqs/statistics/pooling-data-and-chow-tests/.
> > aweights and -xtglm- are discussed, but neither is applicable in this
> > context so I'm turning to the Statalist for assistance.
> >
> > Put as concisely as I can my questions are:
> > 1. Is unequal variance between groups as much of a problem in Poisson
> > models as in linear regression? (Clearly I think "yes" or I wouldn't
> > be posting, but I'd like to verify with more expert folks than me).
> > 2a. Can I control for this in a "pooled" multilevel Poisson model (in Stata)?
> > 2b. How do I control for unequal variance in a pooled multilevel
> > Poisson model in Stata?
> >
> > Here is an example that resembles my problem. Assume for the sake of
> > argument that a group*age interaction is somehow meaningful and
> > interesting in this context.
> >
> > *** begin example ***
> > use  http://www.stata-press.com/data/r12/epilepsy
> >   /* create artificial groups, 1 for odd ID number, 0 for even */
> > gen foo = ceil((subject/2)-int(subject/2))
> >   /* demonstrate baseline differences in variances by group */
> > by subject, sort: gen first=_n==1
> > sdtest seizures if first, by(foo)  /* significant at alpha=0.10, in
> > actual data, p < 0.001 */
> >   /* -xtmepoisson- model from manual for each group (1) */
> > by foo, sort : xtmepoisson seizures treat lage lbas lbas_trt v4, || subject:
> >   /* -xtmepoisson- with interactions for covariate of interest (2) */
> > xtmepoisson seizures treat lage##i.foo lbas lbas_trt v4, || subject:
> >   /* -xtmepoisson- fully interacted (3) (will switch to Laplace here
> > by default) */
> > gen cons0=foo==0
> > xtmepoisson seizures cons0 i.foo##i.treat c.lage##i.foo c.lbas##i.foo
> > c.lbas_trt##i.foo c.v4##i.foo, nocons || subject: R.foo
> >
> > *** end example ***
> >
> > (3) seems to me to be clearly preferred to (2) because it recovers all
> > FEs from (1) though the estimates are not exact. I tried Laplace in
> > both and it didn't make a difference, which from the manual should
> > have been expected. Am I on the right track with this progression? How
> > do I accommodate the fact that the variance in number of seizures
> > differs by "foo"?
> >
> > In case the following is relevant to anyone's recommendations:
> > - The example above only has 59 patients; I have several of thousand.
> > - I do not have an equal number of patients in each group; there is
> > about a 3:1 ratio of 0s to 1s for my comorbidity indicator.
> > - The data is observational. It comes from medical records review.
> > - There are about 30 coefficients to be estimated before any interactions/REs.
> > - There is no randomly assigned treatment, just a set of 3 covariates
> > that I am interested in testing whether they are jointly different
> > between the two groups.
> > - The example data doesn't have a natural level 3 variable, but I have
> > a random intercept for the clinic also.
> >
> > Related econometric references are welcomed just as much as Stata tips
> > because I'd really like to learn more about this. I've tried searching
> > with the terms "pooling Poisson multilevel mixed effects" and various
> > combinations thereof and haven't found anything that addresses the use
> > of pooled data in a Poisson regression let alone the issue of unequal
> > variances.
> >
> > * I'm not sure if the use of R.foo is correct for the RE in model (3).
> > It is my best guess for now & I intend to do more reading on that
> > later.
> >
> > Thanks,
> > Rebecca
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> >
> >
> >
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