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

 From John Antonakis To statalist@hsphsun2.harvard.edu Subject Re: AW: st: AW: beta coefficients for interaction terms Date Sun, 21 Jun 2009 14:55:00 +0200

```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 slength = std(length)
. egen smpg = std(mpg)
. 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

```
```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

```
```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
. reg mpg head length ia, beta

you should code

. sysuse auto, clear
. egen slength = std(length)
. egen smpg = std(mpg)
. 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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kohler@wzb.eu
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