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From |
William Buchanan <[email protected]> |

To |
[email protected] |

Subject |
Re: st: Relative Importance of predictors in regression |

Date |
Wed, 6 Nov 2013 13:38:20 -0600 |

Hi Sam, By its very definition a constant does not vary. So unless you've sampled only males with a varying number of years of schooling, you have not held gender constant; you may have adjusted your estimates for the influence of being a male, but this is not the same. I would argue that in the best of cases, your illustration below indicates that you've included a sex fixed-effect. Billy On Nov 6, 2013, at 1:22 PM, Lucas <[email protected]> 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 > > On Wed, Nov 6, 2013 at 9:08 AM, Richard Goldstein > <[email protected]> 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 >>> <[email protected]> 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 >> * >> * For searches and help try: >> * http://www.stata.com/help.cgi?search >> * http://www.stata.com/support/faqs/resources/statalist-faq/ >> * http://www.ats.ucla.edu/stat/stata/ > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Relative Importance of predictors in regression***From:*Nikos Kakouros <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*Lucas <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*David Hoaglin <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*Lucas <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*David Hoaglin <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*Lucas <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*David Hoaglin <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*Lucas <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*David Hoaglin <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*Lucas <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*David Muller <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*Lucas <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*Richard Goldstein <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*Lucas <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*Richard Goldstein <[email protected]>

**Re: st: Relative Importance of predictors in regression***From:*Lucas <[email protected]>

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