"Case, Brad" wrote:
>
> > Hello. I am hoping that my question can be answered by a statistical
> > expert out there!! (which I am not). I am carrying out a multiple linear
> > regression with two independents. It seems that a square root
> > transformation of the dependent variable effectively decreases
> > heterocscedasticity and "linearises" the data. However, from what I have
> > read, transformations of the dependent variable introduces a bias into the
> > regression, producing improper estimates after back-transforming to "real"
> > units. Does anybody out there have any knowledge of this problem, or have
> > a strategy for correcting for this type of bias? Any help would be much
> > appreciated. Thanks.
It depends on what you mean by a bias.
The OLS regression line minimizes a certain measure of badness-of-fit
over all linear fits to the data. If the dependent variable is
transformed, OLS fitting is done, and the data and line are transformed
back, the new fit will *not* be optimal by that criterion.
On the othe rhand, it will be optimal by some different criterion. The
question is, which criterion do you want and why? The answer "because
all the other researchers are using it" is not adequate. If all the
other researchers jumped off a cliff, etc, etc Nor is the
rhetorically loaded word "bias" a reason to avoid using a method.
Technically, it just means that the curve given isn't what another
method would have given.
The usual *informed* reason for OLS fitting is that with a
homoscedastic normal error model it is the maximum-likelihood estimate
for the parameters of the line. If your data do not support such an
error model, then that reason doesn't apply.
If after transforming the dependent variable the data *do* fit a
homoscedastic normal error model, then within that family of conditional
distributions the maximum likelihood choice *is* the one obtained by OLS
fitting to the transformed data. In other words, the reason that often
justifies OLS fitting justifies, in this case, precisely the transformed
fit that you obtained.
So if your transformed data fit the criteria for OLS fitting, fit them
and transform back, and don't worry about "bias".
-Robert Dawson
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