haenl...@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.
I haven't read that article, but there are many others that demonstrate
that, in cases of *structural* collinearity (polynomial models, models
with interaction terms), mean centering of the Xs, particularly in the
product terms *does* reduce the impact of collinearity to usually
acceptable levels.
Plus, if you mean center the Xs themselves, their coefficients have more
sensible interpretations (slope for X1 at the mean, rather than over the
origin).
-Michael
On Aug 3, 2010 3:42pm, David Winsemius <dwinsem...@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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David Winsemius, MD
West Hartford, CT
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--
Michael Friendly Email: friendly AT yorku DOT ca
Professor, Psychology Dept.
York University Voice: 416 736-5115 x66249 Fax: 416 736-5814
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