Re: st: Relative Importance of predictors in regression

[Stuart Buck <stuartbuck@gmail.com>]

My understanding:

If we estimate this:

y=b1*YrsSchl + b2*Male

then b1 tells us the average effect of years of school across both
males and females.

If we instead estimate this:

y = b1*YrsSchl + b2*Male + b3*YrsSchl*Male

then b1 tells us the effect of years of school for females, b2 tells
us the effect of being male vs. female, and b1 + b3 tells us the
effect of years of school for males (i.e., the b1 effect for females
plus b3, which is the additional impact of years of school, in either
direction, for males).


On Wed, Nov 6, 2013 at 2:02 PM, Stuart Buck <stuartbuck@gmail.com> wrote:
>
> My understanding:
>
> If we estimate this:
>
> y=b1*YrsSchl + b2*Male
>
> then b1 tells us the average effect of years of school across both males and females.
>
> If we instead estimate this:
>
> y = b1*YrsSchl + b2*Male + b3*YrsSchl*Male
>
> then b1 tells us the effect of years of school for females, b2 tells us the effect of being male vs. female, and b1 + b3 tells us the effect of years of school for males (i.e., the b1 effect for females plus b3, which is the additional impact, in either direction, for males).
>
>
> On Wed, Nov 6, 2013 at 1:52 PM, Lucas <lucaselastic@gmail.com> wrote:
>>
>> 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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>
>
>
>
> --
> Stuart Buck
> http://about.me/stuartbuck
> 479-200-2750 (cell)
>



-- 
Stuart Buck
http://about.me/stuartbuck
479-200-2750 (cell)

*
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