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RE: AW: st: AW: beta coefficients for interaction terms


From   "Ploutz-Snyder, Robert (JSC-SK)[USRA]" <robert.ploutz-snyder-1@nasa.gov>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   RE: AW: st: AW: beta coefficients for interaction terms
Date   Thu, 16 Apr 2009 15:13:20 -0500

Statalisters;
I don't have this text but am following the thread.

If I understand Uli's interpretation of this, standardizing predictors before creating interaction terms is deemed relevant if your interests are comparing predictors' effects for change-in-y, and that this is not important for significance testing, or for beta estimates (and their confidence intervals).  

If so, and if you do have an interest in comparing the independent variance contribution of predictors, wouldn't squared semi-partial correlation coefficients handle that with or without standardizing predictors?  Even with an interaction term in the model, sr2 should parse out the unique contributions among the predictors (per Tabachnick and Fidell's discussion in their 1989 text (p.152), Using Multivariate Statistics (2nd Ed)).



Rob

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Ulrich Kohler
Sent: Thursday, April 16, 2009 9:02 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: AW: st: AW: beta coefficients for interaction terms

I think Lisa refer the section on standardized regression cofficients of
that book, particularly to the second item on pg. 201 (English edition).
That item states that one should not use b*s_x/s_y to create
standardized regression coefficients in the presence of interaction
terms. Based on Aiken/West 1991 (28-48) it is recommended that one
should standardize all variables that are part of the interaction in
advance. Hence, instead of coding

. sysuse auto, clear
. gen ia = head*length
. reg mpg head length ia, beta

you should code 

. sysuse auto, clear
. egen shead = std(headroom)
. egen slength = std(length)
. egen smpg = std(mpg)
. gen ia2 = shead*slength
. egen sia2 = std(ia2)
. reg smpg shead slength sia2

The estimated coefficients of the constituent effects then show how much
standard deviations the dependend variable change when the independent
variable changes by one standard deviation and the other variable of the
interaction term is at its mean.

Standardized regression coefficients are often used to find out which of
the independent variables have the "largest" effect. I must admit that I
often fail to understand why students want to know that. But leaving
that aside, if an effect is not constant over the range of another
variable (i.e. in the presence of an interaction term) the question of
which independent variable have the largest effect seems pointless. 


Many regards
Uli


Am Donnerstag, den 16.04.2009, 14:47 +0200 schrieb Martin Weiss:
> <> 
> 
> Your -gen- statement computes the interaction, but Stata would treat this
> new variable as a covariate in its own right, w/o any connection to other
> covariates. A similar issue arises with quadratic terms of a covariate
> (http://www.stata.com/statalist/archive/2008-08/msg00307.html).
> 
> 
> The book you mentioned has a subsection on the topic on pages 222-226, and
> the English version seems to be a straightforward translation of it, AFAIK
> (http://www.stata-press.com/books/daus2.html, page 222). I cannot find the
> stuff on the beta coefficient there, though. They do say that you should
> check for missings with -rowmiss- and that you should subtract the mean from
> the variables before standardization. The latter is easily accomplished via
> 
> *****
> sysuse auto, clear
> 
> *enter your vars to be standardized here
> local stdvars "price weight trunk turn"
> 
> foreach var of local stdvars{
> summ `var', mean
> gen std`var'=`var'-r(mean)
> }
> *****
> 
> -egen, std()- would divide by the standard deviation in addition to my
> code...
> 
> HTH
> Martin
> 
> 
> -----Ursprüngliche Nachricht-----
> Von: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von
> lschoele@rumms.uni-mannheim.de
> Gesendet: Donnerstag, 16. April 2009 14:07
> An: statalist@hsphsun2.harvard.edu
> Betreff: Re: st: AW: beta coefficients for interaction terms
> 
> How do I tell stata, that it is an inetraction term?
> Here is what I did:
> gen appearance_attention=apperance*attention
> 
> Is that telling stata, that the new variable is an interaction term?
> 
> I am referring to the book "Datenanalyse mit Stata" by Kohler, Kreuter
> 
> "Note that you can effect the standardization yourself via - egen,  
> std()-" What standardization do you mean? The z-standardization or the  
> "normal" standardization for the beta coefficients, that I need for  
> the interpretation?
> 
> Best Lisa
> 
> 
> Zitat von Martin Weiss <martin.weiss1@gmx.de>:
> 
> > <>
> >
> > Well, did you tell Stata in any way that a specific variable is an
> > "interaction term"? If not, Stata probably treats it as just another
> > covariate in your regression.
> >
> > BTW, which book are you referring to?
> >
> > Note that you can effect the standardization yourself via - egen, std()-
> >
> >
> > HTH
> > Martin
> >
> > -----Ursprüngliche Nachricht-----
> > Von: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von
> > lschoele@rumms.uni-mannheim.de
> > Gesendet: Donnerstag, 16. April 2009 12:35
> > An: statalist@hsphsun2.harvard.edu
> > Betreff: st: beta coefficients for interaction terms
> >
> > Hi Statalist,
> >
> > I am working on a regression model with interactions between some
> > variables. I read in a book, that I can't use the "normal"
> > standardized beta coefficients for the interaction terms. They said
> > that the interpretation of the beta coefficients is not possible until
> > you z-standardise the interaction variables before you do the
> > regression.
> >
> > Does anyone know, if stata does the z-standardization for the
> > interaction variables automatically, so I can use the normal
> > standardized beta coefficients (shown in the stata output) for the
> > interpretation?
> > I am using the 9.1 version of stata.
> >
> > I hope someone can help me.
> >
> > Best Lisa
> >
> > *
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> 
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-- 
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030 25491-361


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