st: xtmixed: baffling random component

[Peter Goff <peter.t.goff@vanderbilt.edu>]

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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