Monday, March 06, 2006

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

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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