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st: Regression with errors on dependent and independent variables


From   Nicholas Hall <nicholasronhall@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Regression with errors on dependent and independent variables
Date   Tue, 14 Aug 2012 12:44:35 -0700

Dear Stata users,

I'm wondering if I could get some help with how to do a regression in which both my dependent and independent variables have errors.  I'm aware of regression with aweights but aweights only assign a relative weight to each data point (i.e., the relative size of the errors) whereas I want give the absolute size of the errors.  Here is a concrete example in which the dependent and independent variables are averages and thus their errors are simply the standard error of the means.

Say I have a distribution of x and y values for a set of groups defined by the categorical variable group and I calculate the means and standard deviations of each of these groups as follows:
	. collapse (mean) meanx=x (sd) sdx=x (count) nx=x (mean) meany=y (sd) sdy=y (count) ny=y, by(group)

So now each observation corresponds to a group of observations and I calculate the standard error of the mean for each group:
	gen semx = sdx/nx
	gen semy = sdy/ny

Now I would like to run the regressing taking into consideration the errors for each group which may be quite different for different groups.  In my ideal world I would just do something like:
	reg y x, [yerror=semy] [xerror=semx]

Thank you for your help!
Nicholas

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