On May 11, 2011, at 6:26 PM, Matthew Keller wrote:

> Not to rehash an old statistical argument, but I think David's reply

> here is too strong ("In the presence of interactions there is little

> point in attempting to assign meaning to individual coefficients.").

> As David notes, the "simple effect" of your coefficients (e.g., a) has

> an interpretation: it is the predicted effect of a when b, c, and d

> are zero. If the zero-level of b, c, and d are meaningful (e.g., if

> you have centered all your variables such that the mean of each one is

> zero), then the coefficient of a is the predicted slope of a at the

> mean level of all other predictors...

And there is internal evidence that such a procedure was not performed

in this instance. I think my advice applies here.

--

David.

>

> Matt

>

>

>

> On Wed, May 11, 2011 at 2:40 PM, Greg Snow <

[hidden email]>

> wrote:

>> Just to add to what David already said, you might want to look at

>> the Predict.Plot and TkPredict functions in the TeachingDemos

>> package for a simple interface for visualizing predicted values in

>> regression models.

>>

>> These plots are much more informative than a single number trying

>> to capture total effect.

>>

>> --

>> Gregory (Greg) L. Snow Ph.D.

>> Statistical Data Center

>> Intermountain Healthcare

>>

[hidden email]>> 801.408.8111

>>

>>

>>> -----Original Message-----

>>> From:

[hidden email] [mailto:r-help-bounces@r-

>>> project.org] On Behalf Of David Winsemius

>>> Sent: Wednesday, May 11, 2011 7:48 AM

>>> To: Michael Haenlein

>>> Cc:

[hidden email]>>> Subject: Re: [R] Total effect of X on Y under presence of

>>> interaction

>>> effects

>>>

>>>

>>> On May 11, 2011, at 4:26 AM, Michael Haenlein wrote:

>>>

>>>> Dear all,

>>>>

>>>> this is probably more a statistics question than an R question but

>>>> probably

>>>> there is somebody who can help me nevertheless.

>>>>

>>>> I'm running a regression with four predictors (a, b, c, d) and all

>>>> their

>>>> interaction effects using lm. Based on theory I assume that a

>>>> influences y

>>>> positively. In my output (see below) I see, however, a negative

>>>> regression

>>>> coefficient for a. But several of the interaction effects of a with

>>>> b, c and

>>>> d have positive signs. I don't really understand this. Do I have to

>>>> add up

>>>> the coefficient for the main effect and the ones of all interaction

>>>> effects

>>>> to get a total effect of a on y? Or am I doing something wrong

>>>> here?

>>>

>>> In the presence of interactions there is little point in

>>> attempting to

>>> assign meaning to individual coefficients. You need to use predict()

>>> (possibly with graphical or tabular displays) and produce

>>> estimates of

>>> one or two variable at relevant levels of the other variables.

>>>

>>> The other aspect about which your model is not informative, is the

>>> possibility that some of these predictors have non-linear

>>> associations

>>> with `y`.

>>>

>>> (The coefficient for `a` examined in isolation might apply to a

>>> group

>>> of subjects (or other units of analysis) in which the values of `b`,

>>> `c`, and `d` were all held at zero. Is that even a situation that

>>> would occur in your domain of investigation?)

>>>

>>> --

>>> David.

>>>>

>>>> Thanks very much for your answer in advance,

>>>>

>>>> Regards,

>>>>

>>>> Michael

>>>>

>>>>

>>>> Michael Haenlein

>>>> Associate Professor of Marketing

>>>> ESCP Europe

>>>> Paris, France

>>>>

>>>>

>>>>

>>>> Call:

>>>> lm(formula = y ~ a * b * c * d)

>>>>

>>>> Residuals:

>>>> Min 1Q Median 3Q Max

>>>> -44.919 -5.184 0.294 5.232 115.984

>>>>

>>>> Coefficients:

>>>> Estimate Std. Error t value Pr(>|t|)

>>>> (Intercept) 27.3067 0.8181 33.379 < 2e-16 ***

>>>> a -11.0524 2.0602 -5.365 8.25e-08 ***

>>>> b -2.5950 0.4287 -6.053 1.47e-09 ***

>>>> c -22.0025 2.8833 -7.631 2.50e-14 ***

>>>> d 20.5037 0.3189 64.292 < 2e-16 ***

>>>> a:b 15.1411 1.1862 12.764 < 2e-16 ***

>>>> a:c 26.8415 7.2484 3.703 0.000214 ***

>>>> b:c 8.3127 1.5080 5.512 3.61e-08 ***

>>>> a:d 6.6221 0.8061 8.215 2.33e-16 ***

>>>> b:d -2.0449 0.1629 -12.550 < 2e-16 ***

>>>> c:d 10.0454 1.1506 8.731 < 2e-16 ***

>>>> a:b:c 1.4137 4.1579 0.340 0.733862

>>>> a:b:d -6.1547 0.4572 -13.463 < 2e-16 ***

>>>> a:c:d -20.6848 2.8832 -7.174 7.69e-13 ***

>>>> b:c:d -3.4864 0.6041 -5.772 8.05e-09 ***

>>>> a:b:c:d 5.6184 1.6539 3.397 0.000683 ***

>>>> ---

>>>> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

>>>>

>>>> Residual standard error: 7.913 on 12272 degrees of freedom

>>>> Multiple R-squared: 0.8845, Adjusted R-squared: 0.8844

>>>> F-statistic: 6267 on 15 and 12272 DF, p-value: < 2.2e-16

>>>>

>>>> [[alternative HTML version deleted]]

>>>>

>>>> ______________________________________________

>>>>

[hidden email] mailing list

>>>>

https://stat.ethz.ch/mailman/listinfo/r-help>>>> PLEASE do read the posting guide

http://www.R-project.org/posting->>> guide.html

>>>> and provide commented, minimal, self-contained, reproducible code.

>>>

>>> David Winsemius, MD

>>> West Hartford, CT

>>>

>>> ______________________________________________

>>>

[hidden email] mailing list

>>>

https://stat.ethz.ch/mailman/listinfo/r-help>>> PLEASE do read the posting guide

http://www.R-project.org/posting->>> guide.html

>>> and provide commented, minimal, self-contained, reproducible code.

>>

>> ______________________________________________

>>

[hidden email] mailing list

>>

https://stat.ethz.ch/mailman/listinfo/r-help>> PLEASE do read the posting guide

http://www.R-project.org/posting-guide.html>> and provide commented, minimal, self-contained, reproducible code.

>>

>

>

>

> --

> Matthew C Keller

> Asst. Professor of Psychology

> University of Colorado at Boulder

> www.matthewckeller.com

David Winsemius, MD

West Hartford, CT

______________________________________________

[hidden email] mailing list

https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide

http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.