Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of David Winsemius
> Sent: Wednesday, May 11, 2011 7:48 AM
> To: Michael Haenlein
> Cc: r-help at r-project.org
> 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]]
> >
> > ______________________________________________
> > R-help at r-project.org 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
>
> ______________________________________________
> R-help at r-project.org 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.