Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

From |
Lucas <[email protected]> |

To |
[email protected] |

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

Date |
Mon, 4 Nov 2013 15:05:29 -0800 |

I asked my question because you wrote: > The "held constant" part of that interpretation > is not correct. Straightforward mathematics shows that it does > not reflect the way that multiple regression actually works I presumed you had a mathematical representation of the two interpretations and could then show that the former is wrong because the actual regression model is accurately represented by the latter. However, instead of a formula, you provided more text, which is necessarily somewhat imprecise. For example, you keep talking about change. I could pound on that, because in cross-sectional data--the dominant form of data people use with regression modeling--nothing is changing. The values *differ* across cases; they do not change. So, your interpretation of the coefficient as representing change in Y associated with change in X is, it would seem, wrong--the coefficient represents the *difference* in Y associated with a *difference* in X. These observations are not trivial. If I regress cross-sectional son's height on father's height, that does not mean stretching the father will raise the son's height. However, if *change* were truly implicated by the coefficient it would. But, instead of writing in every time you say this I just presume you really understand there is no *change* going on and you are simplifying (or maybe slipping) during a discussion amongst knowledgeable users of the method. Which leads me back to my question. Setting the issue of change vs. difference aside, I still wonder: what is the mathematical representation that makes it clear that your interpretation is right and "held constant" is absolutely wrong? Thanks a bunch! Sam On Mon, Nov 4, 2013 at 2:28 PM, David Hoaglin <[email protected]> wrote: > Hi, Sam. > > I'm not sure what you mean by "the mathematical expression for 'held > constant,'" other than setting each of the other predictors to some > particular value. > > The general interpretation of the coefficient of a predictor in a > multiple regression is that it tells how the dependent variable > changes per unit increase in that predictor, adjusting for > simultaneous linear change in the other predictors in the data at > hand. If the model has n observations on Y and p predictors > (including the constant, if present), and the data on the predictors > form the columns of the (full-rank) matrix X, the mathematics of > ordinary least squares involves projecting Y on the subspace of > n-space spanned by the columns of X. Nothing in that process of > projection holds the other predictors constant at particular values. > > Regards, > > David Hoaglin > > On Mon, Nov 4, 2013 at 3:39 PM, Lucas <[email protected]> wrote: >> What would be the mathematical expression for "held constant"? And >> what is the mathematical expression to which you are comparing it that >> leads you to reject "held constant"? >> >> Thanks a bunch! >> >> 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/

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

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

- Prev by Date:
**Re: st: Mata order() indeterminate** - Next by Date:
**Re: st: Saving variable response sets over many datasets** - Previous by thread:
**Re: st: Relative Importance of predictors in regression** - Next by thread:
**Re: st: Relative Importance of predictors in regression** - Index(es):