Re: st: Relative Importance of predictors in regression

[Lucas <lucaselastic@gmail.com>]

On Rich's point, of course if we estimate:

0. y=b1*YrsSchl + b2*Male
1. y=g1*YrsSchl + g2*Male + g3*white
2. y=h1*YrsSchl + h2*Male + h3*white + h4*age

we would not expect b1=g1=h1 necessarily.  This has nothing to do with
whether we have "held constant" the variables that are in model 0 when
we are interpreting b1.

On William's point, yes, the data has men and women in the example,
else no expected values could be obtained for Y3 and Y4 in the
example. So, paraphrasing William, he says, "You have adjusted your
estimates for gender." Given that claim, what is the correct
interpretation of b1 in model 0 above?  Sounds like you'd say "b1 is
the difference in Y associated with a one year difference in YrsSchl,
once the association between Y and sex has been accounted for." So,
basically, this phrasing reduces to "b1 tells us the association once
we hold constant all the other variables in the model, i.e.,
differences in those variables DO NOT EFFECT our estimate of b1."
[Note: if we interacted sex and education this interpretation would be
inappropriate]. This is what I people mean when they say "held
constant."

It is interesting that there are varying interpretations of David H.'s
point, which suggests his point escapes some and perhaps many.  I
wonder if the formula he mentioned would clarify everything.

Sam

On Wed, Nov 6, 2013 at 11:37 AM, Richard Goldstein
<richgold@ix.netcom.com> wrote:
> Hi Sam,
>
> a little more seriously, consider the following two models:
>
> 1. y=b0 + b1*age + b2*female + b3*white
> 2. y=b0 + b1*age + b2*female
>
> so, there is no reason to expect that either b1 or b2 would be the same
> in these two models -- that I think is (part of) David's point
>
> I don't understand the "hold constant" part and how it might apply here,
> or, really elsewhere when talking about the "effect" of a
> right-hand-side variable; but I don't think that is what you are talking
> about; so, I think that at least part of this discussion has people
> talking past each other. Further, I don't think that this discussion is
> related to the subject line either.
>
> Rich
>
> On 11/6/13, 2:22 PM, Lucas wrote:
>> Hi Rich,
>>
>> Depends on which of us you ask.  I'd say if you compare a male w/ 9
>> YrsSchl and a male w/ 8YrsSchl you've held sex constant and b1 is the
>> difference in Y associated with that one year difference in schooling.
>>  I think David H. would say that you've held nothing constant.  Is
>> that a correct interpretation of your claim, David H.?
>>
>> Sam
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