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


From   Rebecca Pope <rebecca.a.pope@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: "pooled" xtmepoisson with unconstrained error variance
Date   Mon, 26 Nov 2012 08:36:48 -0600

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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