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# RE: st: Multilevel difference modeling with suest

 From Peter Goff To "statalist@hsphsun2.harvard.edu" Subject RE: st: Multilevel difference modeling with suest Date Mon, 19 Mar 2012 15:50:59 -0500

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

Peter
peter.t.goff@vanderbilt.edu
```
```
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```