Re: st: back transform coefficients

[Richard Goldstein <richgold@ix.netcom.com>]

While I generally agree with what Nick and Maarten say here, note that
GLM and regression using a transformation have different assumptions
regarding the distribution of the residuals; if, in your case, the
transformation appears to be better on this ground, then you may want to
use it; for help on back transformation is this case, see Miller, Don M.
(May 1984), "Reducing transformation bias in curve fitting," _The
American Statistician_, 38: 124-126

Rich

On 11/18/11 7:35 AM, Nikolaos Pandis wrote:
> Nick,
>  
> many thanks. It is all clear.
>  
> BW,
>  
> Nick
> 
> 
> ----- Original Message -----
> From: Nick Cox <n.j.cox@durham.ac.uk>
> To: "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
> Cc: 
> Sent: Friday, November 18, 2011 2:05 PM
> Subject: RE: st: back transform coefficients
> 
> No, no. 
> 
> There is no question of an extra back-transformation getting the coefficients on the original scale. The coefficients produced by -glm- are on the original scale. 
> 
> Much of the point of GLMs is that the coefficients have dimensions and units as you would expect; the "transformation" of the response is done by fitting on the scale given by the link function and then, without extra prompting, "undone" by doing the calculations needed to produce predictions, etc., on the original scale. 
> 
> GLMs are not a different way of doing transformations of the response. They are a way to avoid transformation of the response but to do what a transformation would do for you, and thereby to have it both ways, unlikely though that may seem. 
> 
> A better explanation would be tailored to what you are familiar with already, which I don't know. But you may already use e.g. logit models in which you don't follow model fitting with back-transforming the coefficients. 
> 
> Otherwise put, back-transforming is _only_ an awkwardness made necessary by transforming; if you don't transform, you don't need to back-transform. 
> 
> Nick 
> n.j.cox@durham.ac.uk 
> 
> 
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nikolaos Pandis
> Sent: 18 November 2011 11:49
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: back transform coefficients
> 
> 
> Dear Maarten,
>  
> Great, many thanks for the help.
> I assume from your posting that after I run the command I need to follow an extra step in order to get the coeffs in the origninal scale.
> Would you be able to be more specific on how to accomplish this.
>  
> Many thanks,
>  
> Nick
> 
> 
> ________________________________
> From: Maarten Buis <maartenlbuis@gmail.com>
> To: statalist@hsphsun2.harvard.edu 
> Sent: Friday, November 18, 2011 11:52 AM
> Subject: Re: st: back transform coefficients
> 
> On Fri, Nov 18, 2011 at 10:05 AM, Nikolaos Pandis wrote:
>> I am running linear regression with 3 continous and 1 2-level categorical independent variables.
>> The continuous outcome is normally distributed when transformed into sqrt(dep_var).
>> I was wondering how I would be able to back transform the produced coefficients and CIs for interpretation.
> 
> I would not use -regress- to estimate such model, but -glm- with the
> -link(power .5)- option. That way you are modeling the square root
> transformed mean of your dependent variable rather than the mean of
> your square root transformed dependent variable. This makes the
> backtransform much easier, just use -predict-, -margins-, etc.
> 
> Hope this helps,
> Maarten
> 
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
> 
> 
> http://www.maartenbuis.nl
> --------------------------
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