[R] Collinearity in Moderated Multiple Regression

[David Winsemius]

On Aug 3, 2010, at 9:51 AM, haenlein at gmail.com wrote:

> I'm sorry -- I think I chose a bad example. Let me start over again:
>
> I want to estimate a moderated regression model of the following form:
> y = a*x1 + b*x2 + c*x1*x2 + e
>
> Based on my understanding, including an interaction term (x1*x2)  
> into the regression in addition to x1 and x2 leads to issues of  
> multicollinearity, as x1*x2 is likely to covary to some degree with  
> x1 (and x2). One recommendation I have seen in this context is to  
> use mean centering, but apparently this does not solve the problem  
> (see: Echambadi, Raj and James D. Hess (2007), "Mean-centering does  
> not alleviate collinearity problems in moderated multiple regression  
> models," Marketing science, 26 (3), 438 - 45). So my question is:  
> Which R function can I use to estimate this type of model.

 > RSiteSearch("moderation models") # 3 hits

 > RSiteSearch("moderated models") #12 hits

 > RSiteSearch("moderat* models") 139 hits

-- 
David.
>
> Sorry for the confusion caused due to my previous message,
>
> Michael
>
>
>
>
>
>
> On Aug 3, 2010 3:42pm, David Winsemius <dwinsemius at comcast.net> wrote:
> > I think you are attributing to "collinearity" a problem that is  
> due to your small sample size. You are predicting 9 points with 3  
> predictor terms, and incorrectly concluding that there is some   
> "inconsistency" because you get an R^2 that is above some number you  
> deem surprising. (I got values between 0.2 and 0.4 on several runs.
> >
> >
> >
> > Try:
> >
> >  x1
> >  x2
> >  x3
> >
> >
> > y
> > model
> > summary(model)
> >
> >
> >
> > # Multiple R-squared: 0.04269
> >
> >
> >
> > --
> >
> > David.
> >
> >
> >
> > On Aug 3, 2010, at 9:10 AM, Michael Haenlein wrote:
> >
> >
> >
> >
> > Dear all,
> >
> >
> >
> > I have one dependent variable y and two independent variables x1  
> and x2
> >
> > which I would like to use to explain y. x1 and x2 are design  
> factors in an
> >
> > experiment and are not correlated with each other. For example  
> assume that:
> >
> >
> >
> > x1
> > x2
> > cor(x1,x2)
> >
> >
> >
> > The problem is that I do not only want to analyze the effect of x1  
> and x2 on
> >
> > y but also of their interaction x1*x2. Evidently this interaction  
> term has a
> >
> > substantial correlation with both x1 and x2:
> >
> >
> >
> > x3
> > cor(x1,x3)
> >
> > cor(x2,x3)
> >
> >
> >
> > I therefore expect that a simple regression of y on x1, x2 and  
> x1*x2 will
> >
> > lead to biased results due to multicollinearity. For example, even  
> when y is
> >
> > completely random and unrelated to x1 and x2, I obtain a  
> substantial R2 for
> >
> > a simple linear model which includes all three variables. This  
> evidently
> >
> > does not make sense:
> >
> >
> >
> > y
> > model
> > summary(model)
> >
> >
> >
> > Is there some function within R or in some separate library that  
> allows me
> >
> > to estimate such a regression without obtaining inconsistent  
> results?
> >
> >
> >
> > Thanks for your help in advance,
> >
> >
> >
> > Michael
> >
> >
> >
> >
> >
> > Michael Haenlein
> >
> > Associate Professor of Marketing
> >
> > ESCP Europe
> >
> > Paris, France
> >
> >
> >
> >        [[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
> >
> >
> >

David Winsemius, MD
West Hartford, CT