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st: xtmixed: baffling random component

From   Peter Goff <>
Subject   st: xtmixed: baffling random component
Date   Thu, 17 Dec 2009 10:19:34 -0600

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:
       . 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,


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

Peabody #514
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Nashville, TN 37203-5721
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Fax. 615-322-6596

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