From: David Winsemius <dwinsemius_at_comcast.net>

Date: Wed, 11 May 2011 21:45:45 -0400

Date: Wed, 11 May 2011 21:45:45 -0400

On May 11, 2011, at 6:26 PM, Matthew Keller wrote:

> Not to rehash an old statistical argument, but I think David's reply

*> here is too strong ("In the presence of interactions there is little
**> point in attempting to assign meaning to individual coefficients.").
**> As David notes, the "simple effect" of your coefficients (e.g., a) has
**> an interpretation: it is the predicted effect of a when b, c, and d
**> are zero. If the zero-level of b, c, and d are meaningful (e.g., if
**> you have centered all your variables such that the mean of each one is
**> zero), then the coefficient of a is the predicted slope of a at the
**> mean level of all other predictors...
*

And there is internal evidence that such a procedure was not performed in this instance. I think my advice applies here.

-- David.Received on Thu 12 May 2011 - 01:51:17 GMT

>> Matt>>>

> On Wed, May 11, 2011 at 2:40 PM, Greg Snow <Greg.Snow@imail.org>

> wrote:>> 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>>>> 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.>>>> ______________________________________________>> 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.>>>>>> --> Matthew C Keller> Asst. Professor of Psychology> University of Colorado at Boulder> www.matthewckeller.com

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.

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