[R] Total effect of X on Y under presence of interaction effects
David Winsemius
dwinsemius at comcast.net
Thu May 12 03:45:45 CEST 2011
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.
>
> Matt
>
>
>
> On Wed, May 11, 2011 at 2:40 PM, Greg Snow <Greg.Snow at 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
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