### Monday, March 06, 2006

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

Johan HellstrÃ¶m 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

----------------------------------------- CONFIDENTIALITY NOTE: This e-mail message, including any attachment(s), contains information that may be confidential, protected by the attorney-client or other legal privileges, and/or proprietary non-public information. If you are not an intended recipient of this message or an authorized assistant to an intended recipient, please notify the sender by replying to this message and then delete it from your system. Use, dissemination, distribution, or reproduction of this message and/or any of its attachments (if any) by unintended recipients is not authorized and may be unlawful.

* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

Tag: statalist