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st: RE: Multilevel modeling question


From   "Yulia Marchenko" <ymarchenko@stata.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Multilevel modeling question
Date   Fri, 11 Nov 2005 11:54:21 -0600

Allan Garland <agar5858@cox.net> asks how one can take into account
information from higher-level covariates with -xtmixed-:

>I  am trying to model a 2-level problem using -xtmixed-, but cannot find
the >right way to do this from the manual.
>I'm studying hospital resource use for patients cared for by a group of
>doctors (call the resource/dependent variable  COST). I have a number of
>characteristics of the patients that relate to COST (e.g. age, severity of
>illness, etc).
>What I REALLY want to know is the magnitude of the differences among the
>physicians.

Since Alan is interested not only in the variability among doctors but also
the magnitude of the differences among certain doctors he needs to include
physicians as fixed effects in his model.

>I want to look deeper and evaluate the influence of  characteristics of the
>doctors themselves (e.g. their years in practice, board certification
status, >etc) on COST. I do not believe (but am not certain of this) it is
correct to
>just put these doctor-level variables into the fixed-effect equation such
as:
>
>	. xtmixed COST  patient_age severity doc1-docN MD_age || DOCNUM:
>
>or  even
>
>	. xtmixed COST patient_age severity doc1-docN  MD_age || DOCNUM: MD_age
>

Both of the above syntaxes are correct depending on the model formulation.
The first one corresponds to the model with randomly varying intercepts for
each doctor. Also, the regression function is allowed to have different
intercepts for each doctor and take into account effect of a doctor-specific
covariate MD_age. The second syntax, additionally, adds random slopes for
age at doctor levels. However, Allan notes that since each doctor has a
different age the corresponding indicator variables doc1-docN are collinear
with MD_age variable, and one of them is dropped from the model. In this
situation, Allan may be interested in studding the contribution of the
doctor-specific covariate to the variability among COST measurements only:

 . xtmixed COST patient_age severity doc1-docN || DOCNUM: MD_age

Another option Allan may consider is to combine doctors in some age groups
and include the age categories in his model instead of MD_age covariate.

--Yulia
ymarchenko@stata.com


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