Re: st: RE: fitted values in xtmepoisson and xtpoisson

[Dan MacNulty <macn0007@umn.edu>]

Thanks for spotting my error Garry; I did neglect to specify the 
-normal- option. And this highlights my core question: why do the 
marginal fitted values differ so much between poisson models where the 
random effects follow a normal versus a gamma distribution? Moreover, it 
seems the former provide a comparatively poor fit to the observed data. 
Specifically, the marginal fitted values from the poisson model with 
normally distributed random effects appear to underestimate the observed 
counts. This is illustrated with the following code:

. use http://www.stata-press.com/data/r10/epilepsy
. xtset  subject
. xtpoisson seizures lage, re normal
. predict xt_norm, nu0
. xtpoisson seizures lage, re
. predict xt_gamma, nu0
. twoway (lowess seizures lage)  (line xt_norm lage, sort) (line 
xt_gamma lage, sort)

Garry Anderson wrote:
> Dear Dan,
>
> If you use the -,normal- option on the -xtpoisson- model the fitted
> values are the same as -xtmepoisson-. That is, the -xtmepoisson- command
> assumes that the random effects are normally distributed, whereas the
> -xtpoisson- command assumes that they have a gamma distribution. Page
> 286 of the Stata 11 XT manual refers to -xtmepoisson- and says "Because
> this is a simple random-intercept model, you can obtain equivalent
> results by using
> xtpoisson with the re and normal options."
>
> Cheers, Garry
>
>  
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Dan MacNulty
> Sent: Tuesday, 11 May 2010 9:26 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: fitted values in xtmepoisson and xtpoisson
>
> Dear Statalist,
> According to the STATA 10 documentation re:longitudinal/panel data
> (p.264) the model specified as:
>
>     xtmepoisson seizures treat lbas lbas_trt lage visit || subject:
>
> ...is equivalent to this model:
>
>     xtpoisson seizures treat lbas lbas_trt lage visit, re
>
> Yet, the population-averaged fitted values (i.e., predictions that
> include only the fixed portion of the model) appear to differ
> substantially between the two models. For the xtmepoisson model, I
> generated these with the post-estimation command:
>
>     predict newvar, fixedonly
>
> For the xtpossion model, I generated the population-averaged fitted
> values with the post-estimation command:
>
>     predict newvar, nu0
>
> I'd be very grateful if someone could explain why there's an apparent
> difference in the population-averaged fitted values between these two
> purportedly equivalent models.
>
> thanks,
> Dan MacNulty
>
>
>
>
>
>
>
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