RE: st: Multilevel difference modeling with suest

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

Thanks for your thoughts on the modeling the Teacher-Principal (T-P)  
difference. As it turns out, polynomial regression is a great method  
for modeling differences between variables when the differenced  
quantity of interest is an independent variable. However, in the  
situation below I'd like to use a vector of independent variables (X)  
to model/predict the T-P difference as the dependent variable.

T = a + zX + e
P= b + yX + u
(T-P) = (a-b) + (z-y)X + (e+u)

Any comments on whether the method I outline is appropriate for multi- 
level modeling of seemingly unrelated regression and whether I have  
identified the appropriate approach to test for non-zero difference  
between coefficients is kindly appreciated. That is, will this  
approach provide the appropriate standard errors to test:

z = 0
y = 0
(z-y) = 0

To be clear, principal self-evaluations (P) are constant within  
principals but vary between principals. Teacher evaluations of  
principals vary within and between principals. Some of the X variables  
are teacher-level and vary both between and within principals; others  
are principal-level variables and only vary between groups.

Kind thanks,
~Peter
peter.t.goff@vanderbilt.edu

> Hi All,
>
> I'm trying to determine the best way to tackle what has been a bit of
> a slippery problem. My goal is to determine which factors (X) are
> predictive of the difference between how teachers perceive a
> principal's leadership (T) and how the principal perceives their own
> leadership (P). X contains some teacher-level factors (e.g., teacher
> experience) and some principal-level factors (e.g., principal gender).
> The literature suggests that the best approach to this problem is to
> model these equations jointly and then individually test for
> differences between the coefficients in X. To complicate matters
> somewhat, teachers are nested within principals so sureg or mvreg
> can't be used, since neither can accommodate the clustering. I have
> pursued several suggestions from colleagues and archived statalist
> posts (e.g., http://www.stata.com/statalist/archive/2009-04/msg01157.html)
>  that has landed me a bit further from my comfort zone that I'd like.
> I'd like to present what I have done thus far and hear if anyone has
> criticism or alternative suggestions.
>
> reg T X
>      estimates store t1
> reg P X
>      estimates store p1
> suest t1 p1, vce(cluster prinid)
> foreach x in X {
>      test _b[t1_mean:`x'] - _b[p1_mean:`x'] = 0
> }
>
> In terms of an interpretation, I'd like to use the t1_mean equation
> from the suest results to make statements about how each of X factors
> relate to teachers' perceptions of leadership effectiveness; use
> p1_mean suest results to make statements about how each of X factors
> relate to the principals' perceptions of their own leadership
> effectiveness; and use the test results to make statements about how
> each of X factors relate to the teacher - principal gap. Kind thanks
> for your thoughts and insights.
>
> Peter
> peter.t.goff@vanderbilt.edu

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