Re: st: about residuals and coefficients

[Richard Williams <richardwilliams.ndu@gmail.com>]

At 09:26 PM 9/17/2013, David Hoaglin wrote:
> Ronan,
>
> I continue to prefer "per unit increase" since a regression
> coefficient is a type of slope.  In a particular application an actual
> increase of one unit may be too large or too small to be meaningful.
> The exception, of course, arises when the predictor is an indicator,
> whose values are only 0 and 1.
>
> The language about the expected effect of the change on the other
> predictors in the model may not reflect the associations among the
> predictors.
>
> I do not understand teaching the "other things held constant"
> interpretation.  First impressions are often powerful.  It seems a
> disservice to students to teach them an interpretation that is flawed.
>  It simply does not reflect the way that multiple regression works.
>
> David Hoaglin

I am not sure if David would like this any 
better, but I often use phrasings along the lines 
of "On an all other things being equal basis" or 
"if you had two otherwise identical people, one 
male and one female, how would you expect their 
scores to differ?" The "held constant" phrasing 
seems a bit nonsensical for variables like gender 
-- gender can't (or at least usually doesn't) 
change, but it is possible to have people who 
have similar or identical values on the other 
independent variables but who differ in their gender.

The comparisons should be reasonable -- I 
probably would not say something like "If you had 
two otherwise identical people, one a 
multi-billionaire and the other broke and penniless..."



> On Sat, Sep 7, 2013 at 7:16 AM, Ronan Conroy <rconroy@rcsi.ie> wrote:
> > On 2013 MFómh 7, at 01:25, David Hoaglin wrote:
> >
> >> I usually suggest the following wording: The coefficient of Xj is the
> >> average change in Y per unit increase in Xj after adjusting for
> >> simultaneous linear change in the other predictors in the model in the
> >> data at hand.  It would be nice to have something simpler, but in
> >> general nothing simpler will do.  I suggest "per unit increase in Xj"
> >> because the coefficient is a sort of slope, and a change of one unit
> >> may not be meaningful in the particular set of data.
> >
> > Or, if writing for people who think in 
> language: The coefficient of the predictor 
> variable is the change we expect associated 
> with a one-unit increase in the predicted 
> variable, after we adjusted for the expected 
> effect that this change will have on the other 
> predictor variables in the model.
> >
> > Or can someone suggest a better way of phrasing this?
> >
> > Purely pragmatically, I tend to teach the 
> 'other things held constant' interpretation 
> because it's a good first-pass in understanding 
> multivariate models, and it's not doing any 
> real-life violence to the interpretation of the 
> data that I can see (has anyone examples where it's plain misleading?).
> >
> > Ronán Conroy
>
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Richard Williams, Notre Dame Dept of Sociology
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