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RE: Re: st: Total Least Squares Regression, anyone


From   "Steichen, Thomas J." <SteichT@rjrt.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: Re: st: Total Least Squares Regression, anyone
Date   Mon, 6 Mar 2006 11:24:30 -0500

Johan Hellström writes:
> Dear Tero,
> 
> I might have misunderstood your problem, but I think you 
> could use the Stata command for errors-in-variables 
> regression, eivreg, so solve your problem.

In response to Tero Kivel:
> >To fulfil the requirements of standard ANSI Z80.10-2003 I need 
> >to perform "Total Least Squares Regression", not referenced or 
> specified.
> >
> >Is this something that Stata can perform? I found nothing with  
> >the search untility. If so, how?

As a first thought, eivreg seems a reasonable approach.  However, 
the Stata implementation with a single X variable is identical to 
least-squares regression, a la regress, as it forces reliability 
to be 1 with a single X.

An alternative is the reduced-major axis (RMA) equation provided by
program concord. Concord also provides some of the other mentioned
stats. 

A second alternative is to solve for the TLS regression coefficients
by minimizing sum((y - (a + b*x))^2 / (1 + b^2)) over the data.

I'm not sure what is meant by "standard deviation of the regression" 
but I suspect it is just rmse = sqrt(sum(y - yhat)^2/(n-2)), which 
can be computed once you have the slope and intercept.

My impression is that the RMA estimates fall between the TLS and OLS
estimates, but much nearer TLS.

Tom






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