Michael Haenlein
2011-May-11 08:26 UTC
[R] Total effect of X on Y under presence of interaction effects
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?
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]]
David Winsemius
2011-May-11 13:47 UTC
[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