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st: AW: xtmixed: baffling random component


From   "Martin Weiss" <martin.weiss1@gmx.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: AW: xtmixed: baffling random component
Date   Thu, 17 Dec 2009 17:29:20 +0100

<> 


"The second nugget of hope comes from  
the help file within xtmixed. In this file, the first example of a  
random coefficients model is one where the coefficient that varies has  
no level 1 variation."



Not sure what you mean by that. Your "level 1" is, in terms of -h xtmixed-,
the "fe_equation", i.e. the fixed-effects part of the model. And sure
enough, "grade" does appear there, so it is accounted for on your "level 1".
There is not supposed to be any variation there, though - hence the name
"fixed effects".

The first time variation for a coefficient even enters the picture is on
your "level 2", which the help file calls "re_equation", following the
double pipe symbol. 


HTH
Martin


-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Peter Goff
Gesendet: Donnerstag, 17. Dezember 2009 17:20
An: statalist@hsphsun2.harvard.edu
Betreff: st: xtmixed: baffling random component

Hi All

I'm working with a 2-level model (I have teachers within schools); I'm  
using xtmixed to examine this nested model.

Upon a reviewer's insightful suggestion I added a level-2 covariate to  
my model (tch_mean). Owing to my own insomnia,  I mistakenly assumed  
this was a level 1 variable and decided to check to see if there was  
significant variation if I added a random component to this  
coefficient into the model. Lo-and-behold there was. Now I've  
regressed into a little ball of confusion trying to understand why  
this is.

At first I thought I made a moronic mistake (which, I'm aware, may  
still be the case). Two nuggets indicate I may not have. One, stata  
didn't crash or kick out an error when I asked it to allow a level 2  
variable to vary - so apparently it is computationally feasible  
(though it may not be sensible). The second nugget of hope comes from  
the help file within xtmixed. In this file, the first example of a  
random coefficients model is one where the coefficient that varies has  
no level 1 variation. The syntax they use is parallel to my own.

I'm investigating this point because the results generated with this  
level 2 variation are much more interesting than without this  
variation (it changed the magnitude and increased the significance of  
some other level 2 variables). My current understanding of the random  
component doesn't leave any room to accommodate how my situation can  
be explained. I had thought that there needed to be variation within  
the level 1 cluster to allow for a random component (and the level 2  
variables are used to predict the school-specific intercepts). Any  
thoughts you have would be greatly appreciated.

Here's the code from the example in the stata help file:
    Setup
        . webuse nlswork

    Random-intercept and random-slope (coefficient) model, correlated  
random effects
        . xtmixed ln_w grade age c.age#c.age ttl_exp tenure  
c.tenure#c.tenure || id: grade, cov(unstruct)

My code:
. xtmixed gap diff2 tdbkgd3a tch_mean sd pd_gender pdyradm pdyrtch  
pdyrsch enroll_07 econdis_07 tcap_ssm_08 ///
	|| prinid: tch_mean, mle cov(un) var

where prinid identifies schools.

I'm having trouble understanding why this is a methodologically sound  
approach (if I'm correct in inferring this from the similar example  
within the help file). How is giving a level 2 covariate a random  
component understood within a 2-level model?

My second question will likely be explained through an understanding  
of the above, but I'd also like to know why/how allowing this level-2  
to have a random component so drastically changes my other level-2  
variables (at least 3 of them). How do I interpret the other level-2  
variables in light of the significant random variation of tch_mean?

Kind thanks for your insights,

~PG

Peter Trabert Goff
PhD student
Department of Leadership, Policy, and Organizations
Vanderbilt University

Peabody #514
230 Appleton Place
Nashville, TN 37203-5721
Tel. 615-415-7844
Fax. 615-322-6596
peter.t.goff@vanderbilt.edu




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