Re: st: Relative Importance of predictors in regression

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

Hi Sam,

using your example, the effect of comparing a male with 9 years of
schooling to a female with 8 years of schooling is b1, correct? So what
is held constant?

Rich

On 11/6/13, 11:42 AM, Lucas wrote:
> Hi Rich,
> 
> You offer an opportunity that perhaps will help David H. clarify what
> he meant as well.
> 
> Here's the deal--Imagine 4 imaginary people, one male w/ 8 yrs schl,
> one male w/ 9 yrs schl, one female w/ 8 yrs schl, one female w/ 9 yrs
> schl.  Given the following translation of the original model I
> offered:
> 
> Y=b1*YrsSchl+b2*Male
> 
> and according to the "held constant" interpretation, here are the
> following (and correct) expected values:
> 
> 1)    Male, 8 Yrs Schl => E(Y) = b1*8+b2
> 2)    Male, 9 Yrs Schl => E(Y) = b1*9+b2
> 3)Female, 8 Yrs Schl => E(Y) = b1*8
> 4)Female, 9 Yrs Schl => E(Y) = b1*9
> 
> "Hold constanting" sex by comparing males w/ different years of
> schooling--subracting case 1 from case 2 yields:
> 
> E(Y2)-E(Y1)=(b1*9+b2)-(b1*8+b2)
>                    =9b1-8b1
>                    =b1
> 
> "Holding constant" education by comparing males and females with the
> same years of schooling--subtracting case 4 from case 2, yields:
> 
> E(Y2)-E(Y4)=(b1*9+b2)-(b1*9)
>                   =b2
> 
> Thus, the held constant interpretation means that b1 reflects the
> difference in Y associated with a 1 year difference in Yrs Schl, once
> other variable(s) in the model are "held constant", and b2 reflects
> the difference in Y associated with sex, once other variable(s) in the
> model are "held constant."
> 
> David H.'s claims imply the calculations above are incorrect, for he
> claims that we can *never* use the hold constant interpretation.  And
> the hold constant interpretation is embedded in the calculations above
> because, in fact, we are holding constant all the other variables. It
> seems that instead of regarding the model estimation as properly
> accounting for any purely empirical (as opposed to logical, e.g., X
> and X^2) associations between the X's, we have to come back in after
> model estimation and again account for any association between the
> X's.  This is obviously necessary in models for categorical variables,
> which is why one must interpret the magnitude of coefficients in light
> of the location of other variables in the model. But David H. is
> saying this is also true of OLS.
> 
> David H. may be correct.  I am open to being persuaded--I am not
> invested in a particular answer.  But, at this point I remain
> unpersuaded. And a citation to his point would really really help.
> 
> Thanks a bunch!
> Sam
> 
> On Wed, Nov 6, 2013 at 7:43 AM, Richard Goldstein
> <richgold@ix.netcom.com> wrote:
>> Hi,
>>
>> I have not been paying any particular attention to this thread but the
>> most recent contribution caught my eye
>>
>> Sam writes, "In other cases, however, the held constant interpretation
>> seems completely reasonable (e.g., E(Y)=b1*YrsSchl+b2*Sex)"
>>
>> this confuses me: the effect of sex is the same regardless of whether
>> YrsSchl changes or does not change (and also for YrsSchol regardless of
>> whether the value of Sex changes) so how can the "held constant
>> interpretation" be reasonable?
>>
>> Maybe you only typed a shorthand of what you meant but, as worded, I do
>> not agree with you.
>>
>> Rich
>>
>> On 11/6/13, 10:26 AM, Lucas wrote:
>>> David M.,
>>>
>>> Thanks for weighing in.  Maybe your doing so will help out.  Indeed,
>>> what you say is how I have interpreted this issue in the past.
>>> Clearly, in some cases (e.g., X and X^2) one cannot hold one variable
>>> constant and difference the other.  In other cases, however, the held
>>> constant interpretation seems completely reasonable (e.g.,
>>> E(Y)=b1*YrsSchl+b2*Sex). [Parenthetically, this is structurally the
>>> same as saying "change is relevant for some models, impossible to
>>> reference for others"--i.e., content matters.]
>>>
>>> What piqued my interest is David H. indicated he had a mathematical
>>> expression that would straightforwardly show that "held constant" is
>>> always wrong.  Yet, after asking for it for a couple of days, it still
>>> has neither been conveyed nor has a citation been provided (well, two
>>> textbooks were cited, but it was unclear which, if either, had the
>>> expression or just a differently interpretable derivations).  That's
>>> more than a little disappointing.
>>>
>>> Perhaps someone else has the expression.  If so, it'd be great to
>>> either see it or be pointed to where it can be found.
>>>
>>> Or, perhaps there is no such expression.  No disrespect intended.
>>> But, we cannot accept a claim--or expect our students or clients to
>>> accept a claim--on the basis of someone saying, "I have the evidence
>>> here, I just can't show it to you."
>>>
>>> Sam
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