Re: transformation of dependent variable in regression
there is nothing from stopping you (is there?) trying several methods that are seen as sensible possibilities ... and seeing what happens? of course, you might find a transformational algorithm that works BEST (of those you try) with the data you have but ... A) that still might be an "optimal" solution and/or B) it might be "best" with THIS data set but ... for other similar data sets it might not be i think the first hurdle you have to hop over is ... does it make ANY sense WHATSOEVER to take the data you have collected (or received) and change the numbers from what they were in the first place? if the answer is YES to that then my A and B comments seem to apply but, if the answer is NO ... then neither A nor B seem justifiable with 2 independent and 1 dependent variables... you have possibilities for transforming 0 of them ... 1 of them ... 2 of them ... or all of them and, these various combinations of what you do might clearly produce varying results _ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: transformation of dependent variable in regression
"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 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
transformation of dependent variable in regression
> 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. > > Brad. > > === > Brad Case, MScF > Spatial Data Modeller/Analyst > > Canadian Forest Service > Northern Forestry Centre > Landscape Management/Climate Change > 5320-122 St. > Edmonton, AB T6H 3S5 > Phone: 780-435-7384 > Fax: 780-435-7359 > == > > = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
