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

[John Antonakis <john.antonakis@unil.ch>]

Hi:

It depends on what you want. Here is the original regression:

. reg mpg head length ia2,

     Source |       SS       df       MS              Number of obs 
=      74
-------------+------------------------------           F(  3,    70) =   
41.45
      Model |  1563.44248     3  521.147492           Prob > F      =  
0.0000
   Residual |  880.016983    70  12.5716712           R-squared     =  
0.6398
-------------+------------------------------           Adj R-squared =  
0.6244
      Total |  2443.45946    73  33.4720474           Root MSE      =  
3.5457

------------------------------------------------------------------------------
        mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. 
Interval]
-------------+----------------------------------------------------------------
   headroom |  -.1522544    .583323    -0.26   0.795    -1.315655    
1.011147
     length |  -.2065272   .0217639    -9.49   0.000    -.2499339   
-.1631206
        ia2 |   .6077389   .5377608     1.13   0.262    -.4647913    
1.680269
      _cons |   60.25667   3.550618    16.97   0.000     53.17518    
67.33815
------------------------------------------------------------------------------

From the -spost- suite of commands, we get:

. listcoef, std

regress (N=74): Unstandardized and Standardized Estimates

Observed SD: 5.7855032
SD of Error: 3.5456553

-------------------------------------------------------------------------------
        mpg |      b         t     P>|t|    bStdX    bStdY   
bStdXY      SDofX
-------------+-----------------------------------------------------------------
   headroom |  -0.15225   -0.261   0.795  -0.1288  -0.0263  -0.0223     
0.8460
     length |  -0.20653   -9.489   0.000  -4.5986  -0.0357  -0.7948    
22.2663
        ia2 |   0.60774    1.130   0.262   0.4815   0.1050   0.0832     
0.7923
-------------------------------------------------------------------------------

As you can see, standardizing on Xs only, on Y only, and on X's and Y 
gives different coefficients.

When you run

. reg mpg head length ia2, beta

     Source |       SS       df       MS              Number of obs 
=      74
-------------+------------------------------           F(  3,    70) =   
41.45
      Model |  1563.44248     3  521.147492           Prob > F      =  
0.0000
   Residual |  880.016983    70  12.5716712           R-squared     =  
0.6398
-------------+------------------------------           Adj R-squared =  
0.6244
      Total |  2443.45946    73  33.4720474           Root MSE      =  
3.5457

------------------------------------------------------------------------------
        mpg |      Coef.   Std. Err.      t    
P>|t|                     Beta
-------------+----------------------------------------------------------------
   headroom |  -.1522544    .583323    -0.26   0.795                
-.0222636
     length |  -.2065272   .0217639    -9.49   0.000                
-.7948497
        ia2 |   .6077389   .5377608     1.13   0.262                 
.0832287
      _cons |   60.25667   3.550618    16.97   
0.000                        .
------------------------------------------------------------------------------

.......notice that Stata gives you the completely standardized solution 
under "Beta" (and no constant).  It is like running:

. reg smpg shead slength sia2

     Source |       SS       df       MS              Number of obs 
=      74
-------------+------------------------------           F(  3,    70) =   
41.45
      Model |  46.7088988     3  15.5696329           Prob > F      =  
0.0000
   Residual |  26.2911008    70  .375587154           R-squared     =  
0.6398
-------------+------------------------------           Adj R-squared =  
0.6244
      Total |  72.9999996    73  .999999994           Root MSE      =  
.61285

------------------------------------------------------------------------------
       smpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. 
Interval]
-------------+----------------------------------------------------------------
      shead |  -.0222636   .0852974    -0.26   0.795    -.1923839    
.1478566
    slength |  -.7948497   .0837613    -9.49   0.000    -.9619065    
-.627793
       sia2 |   .0832287   .0736453     1.13   0.262    -.0636523    
.2301096
      _cons |  -6.66e-09   .0712426    -0.00   1.000    -.1420888    
.1420888
------------------------------------------------------------------------------

Up to you what to report. If you want to know the relative std. dev. 
changes in the Xs and how they affect Y (in raw units), then standardize 
on X's only.

Best,
J.

____________________________________________________

Prof. John Antonakis
Associate Dean Faculty of Business and Economics
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland

Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305

Faculty page:
http://www.hec.unil.ch/people/jantonakis&cl=en

Personal page:
http://www.hec.unil.ch/jantonakis
____________________________________________________



On 21.06.2009 13:59, lschoele@rumms.uni-mannheim.de wrote:
> Thank you very much.
> I was just a little confused, since in the example I was given the DV 
> was standardized.
>
> Example
>
> 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
>
> Best,
> Lisa
>
> Zitat von John Antonakis <john.antonakis@unil.ch>:
>
> > Hi:
> >
> > As far as I know, there is not reason to standardize the dependent
> > variable (when standardizing the independent variable to obtain their
> > standardized effects).
> >
> > Given the range of the DV will change substantively when standardizing
> > it is evident that the intercept now is qualitatively different from
> > before and might not be different from zero.
> >
> > I'd stick to having the DV in raw units.
> >
> > HTH,
> > J.
> >
> > ____________________________________________________
> >
> > Prof. John Antonakis
> > Associate Dean Faculty of Business and Economics
> > University of Lausanne
> > Internef #618
> > CH-1015 Lausanne-Dorigny
> > Switzerland
> >
> > Tel ++41 (0)21 692-3438
> > Fax ++41 (0)21 692-3305
> >
> > Faculty page:
> > http://www.hec.unil.ch/people/jantonakis&cl=en
> >
> > Personal page:
> > http://www.hec.unil.ch/jantonakis
> > ____________________________________________________
> >
> >
> >
> > On 21.06.2009 12:54, lschoele@rumms.uni-mannheim.de wrote:
> > > Hi
> > >
> > > but it is important for my paper to show the value of the  
> > > intercept, and I get different values if I use either the  
> > > standardized or the not standardized dependent variable. If I have  
> > > the null hypothesis that is is equal to zero, do I have to use the  
> > > standardized or not standardized dependent variable? And coming  
> > > back to my original question: Why do I have to standardize the  
> > > dependent variable?
> > >
> > > Best,
> > > Lisa
> > >
> > >
> > > Zitat von Alan Neustadtl <alan.neustadtl@gmail.com>:
> > >
> > > > If it is not meaningful for your paper how is that complete.  I am
> > > > sure yo ucould think of other things to include for "completeness" but
> > > > you left out.  In general the null hypothesis for the intercept is
> > > > that it is equal to zero.  If that is unimportant it is not needed.
> > > >
> > > > Best,
> > > > Alan
> > > >
> > > >
> > > > On Sat, Jun 20, 2009 at 10:26 AM, <lschoele@rumms.uni-mannheim.de> 
> > > > wrote:
> > > > > Hi Alan,
> > > > >
> > > > > I do not have a hypothesis for the intercept, but I want to show the
> > > > > significance in my paper due to completeness.
> > > > >
> > > > > Best,
> > > > > Lisa
> > > > >
> > > > >
> > > > > Zitat von Alan Neustadtl <alan.neustadtl@gmail.com>:
> > > > >
> > > > > > In your case what is your null hypothesis regarding the intercept?
> > > > > > Why do you want to test for significant difference of this estimate
> > > > > > and some other value?
> > > > > >
> > > > > > In many cases the intercept is 1) beyond the range of the data (and
> > > > > > therefore a poor estimate), and 2) theoretically uninteresting.
> > > > > >
> > > > > > Best,
> > > > > > Alan
> > > > > >
> > > > > >
> > > > > > On Sat, Jun 20, 2009 at 8:51 AM, <lschoele@rumms.uni-mannheim.de> 
> > > > > > wrote:
> > > > > > > Hi Statalist,
> > > > > > >
> > > > > > > I have one more question regarding this theme.
> > > > > > > Why do I have to standardize the dependent variable as well? If I
> > > > > > > standardize it, the constant won't be significant anymore. Without
> > > > > > > standardizing the constant is highly significant in my case.
> > > > > > >
> > > > > > > Thank you
> > > > > > > Lisa
> > > > > > >
> > > > > > > Zitat von Ulrich Kohler <kohler@wzb.eu>:
> > > > > > >
> > > > > > > > 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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