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st: Accounting for measurement error in regression


From   "Jason Becker" <Jason.Becker@ride.ri.gov>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Accounting for measurement error in regression
Date   Wed, 20 Oct 2010 16:47:16 -0400

Hello,

My data has measurement error which is generally modeled as following a
Bernoulli distribution.  The data are percentages of students at a
school who score above a cutoff point on an exam, and the error is
modeled as sqrt((p)*(q)/N) where p = percentage of students above the
cutoff, q = percentage of students below the cutoff, and N is the number
of students).

Typically I've run regressions which assume that the percentage of
students above this cutoff is the true value for each school.  I'd like
to take into account the error in assigning students to one category or
another, but the methods described when I searched online
(http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter4/statareg4.htm)
are only applicable to constant measurement error.

Is there some way for me to take this error into account in my model?  

I believe that if I calculate a regression without taking into account
this error, it is inappropriate to apply the error bars around each
observation after the fact because the model is constructed under the
assumption that the sample data is accurate.  It seems the common
practice has been to construct 95% CI's around each observation after
the regression is run to determine if a school meaningfully deviates
from the regression estimate.  I think the appropriate practice with a
regression run without the error assumptions would be to construct an
error region around the regression estimate itself and treat the school
data as fixed.

Thanks in advance for your help.

Jason

_____
Jason Becker
Research Specialist
Office of Data Analysis and Research
Rhode Island Department of Education
255 Westminster Street Providence, RI 02903
(401)-222-8495


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