[R] Total effect of X on Y under presence of interaction effects

[Greg Snow]

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
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
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> > 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.