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 |
David Hoaglin <[email protected]> |

To |
[email protected] |

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

Date |
Tue, 5 Nov 2013 12:26:15 -0500 |

Dear Sam, It would help communication if you explained, as specifically as possible, what sort of "mathematical expression" you are looking for. The material in my previous message that you reject as a "mathematical manipulation" needs only one further step, involving straightforward algebra: In the result of regressing the Y-residuals on the X2-residuals, multiply out the right-hand side, rearrange the equation to leave only Y on the left-hand side, and compare the result term by term against the original model. Since the adjustments for the contributions of the other predictors are shown explicitly, the interpretation of b2 is clear. Please explain how you would interpret the demonstration differently. The fact that regression coefficients are a type of slope does not provide any basis for the "held constant" interpretation. I do not see the connection between a regression model and your analogy of the position of two people on a hill. Please explain further. When you said that I "retain one mis-interpretation of the regression model that is extremely elementary and easily corrected," I assume you are referring to the distinction that you make between "change" and "difference." I explained earlier that I would use words appropriate to the particular context and application, so I am not making any mis-interpretation. I remind you that you have not offered any mathematical expression for the "held constant" interpretation. Regards, David Hoaglin On Tue, Nov 5, 2013 at 9:37 AM, Lucas <[email protected]> wrote: > Hi David, > > I am looking for the mathematical expression you indicated would make > it clear which interpretation is correct. The mathematical > manipulation isn't very helpful, because someone who interprets the > issue differently than you do before can interpret this demonstration > differently than you do. So, do either of those books have the > mathematical expression you mentioned? If so, I'll check it out. > > On change vs. difference, discrete things change or do not, and > non-discrete things change or do not. The distinction between "change > and difference" is orthogonal to the distinction between "discrete and > non-discrete." > > Indeed, the analogy you deploy to support the change interpretation, > using slopes and hills, is one reason people say "held constant." The > difference (slope) between my height on the hill and Joe's height on > the hill is distinct from (and independently estimable given) our > horizontal placement on the hill. Horizontal placement, thus, is "held > constant." If this is incorrect, it shows why analogies are less > helpful than mathematical expressions. Thus, my request for the > mathematical expression you indicated was available. > > I do not understand why you retain one mis-interpretation of the > regression model that is extremely elementary and easily corrected, > but are adamant that everyone else is wrong if they use (what you > call) another mis-interpretation of the model, a mis-interpretation > that 1)can be shown with straightforward mathematical expressions but > then 2)seems so complex that it cannot be written in plain text. > > Anyway, please let me know which of those textbooks have the > mathematical expression you referenced earlier. I'll pull it from the > library and take a look > > Thanks! > > 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/

**Follow-Ups**:

**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]>

**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]>

- Prev by Date:
**Re: st: Relative Importance of predictors in regression** - Next by Date:
**st: Relative Importance of predictors in regression** - Previous by thread:
**Re: st: Relative Importance of predictors in regression** - Next by thread:
**Re: st: Relative Importance of predictors in regression** - Index(es):