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

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