# Adjusting regression coefficient for predictor error

I saw a famous review paper about intelligence, and the authors introduced a way to adjust the regression coefficient for predictor error.

As many of you might know, if the predictor has a measurement error or if it has reliability less than 1, the regression coefficient estimate(OLS) is biased towards 0.(less than the true regression coefficient). But I haven't seen the same method applied among the papers published recently.

So, I wonder if it is still valid method to adjust the biased regression coefficient from measurement error(which is using estimates of variance of error term).

If not, why is it not?

EDIT === Watching Econometrics Lecture, http://www.youtube.com/watch?v=Kb4LvSguwjg&index=12&list=PLD15D38DC7AA3B737 For Econometrics, people use instrumental variables... which is correlated with true independent variables and uncorrelated with error..

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## 1 Answer

If it is known that you have errors in variables and know the variance of the error you should not use least squares to estimate the function. For example if the a variable X has the same variance as the model error component then minimizing the perpendicular distance gives the proper estimate for the regression coefficient. So I prefer to think of the thing to do is to directly get the correct estimate of the coefficient rather than adjusting the least squares estimate.

The error in variables problem has been studied and minimizing the appropriate squared distance is the way to compute the regression coefficients.

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Thank you for the answer. Actually, I anticipated something like that the latent variable approach is free of measurement error. I would like to dig in more, could you give me the references? Anyway, does "the variable X has the same variance as the model error component" above mean the variance of measurement error of the variable X? I guess if the variance of measurement error of both X and Y are equal, perpendicular distance is preferred. – KH Kim Aug 12 '12 at 3:26
I found wiki page for the subject, en.wikipedia.org/wiki/Errors-in-variables_models – KH Kim Aug 12 '12 at 3:42
I see the method is essentially the same as I saw in the paper-Adjusting OLS estimates with reliability of the predictor. Of course if the variance of measurement error of X and the model error component(as you wrote!) is the same, orthogonal regression is recommended. And I still wonder why it is no longer seen much, is it that I read too few papers? – KH Kim Aug 12 '12 at 3:48
@KHKim Good to see that you are finding the information> – Michael Chernick Aug 12 '12 at 4:10