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.

Sorry for the confusion caused due to my previous message,

Michael






On Aug 3, 2010 3:42pm, David Winsemius <dwinsemius@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



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> and provide commented, minimal, self-contained, reproducible code.




> David Winsemius, MD

> West Hartford, CT




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