Re: st: Relative Importance of predictors in regression

[Lucas <lucaselastic@gmail.com>]

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

On Wed, Nov 6, 2013 at 9:08 AM, Richard Goldstein
<richgold@ix.netcom.com> wrote:
> 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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