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.s...@imail.org 801.408.8111 > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-bounces@r- > project.org] On Behalf Of David Winsemius > Sent: Wednesday, May 11, 2011 7:48 AM > To: Michael Haenlein > Cc: r-help@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@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@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. ______________________________________________ R-help@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.
