Thanks very much -- it seems that Ridge Regression can do what I'm looking for! Best, Michael
-----Original Message----- From: Nikhil Kaza [mailto:nikhil.l...@gmail.com] Sent: Tuesday, August 03, 2010 16:21 To: haenl...@gmail.com Cc: r-help@r-project.org (r-help@R-project.org) Subject: Re: [R] Collinearity in Moderated Multiple Regression My usual strategy of dealing with multicollinearity is to drop the offending variable or transform one them. I would also check vif functions in car and Design. I think you are looking for lm.ridge in MASS package. Nikhil Kaza Asst. Professor, City and Regional Planning University of North Carolina nikhil.l...@gmail.com On Aug 3, 2010, at 9:51 AM, 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. > > Sorry for the confusion caused due to my previous message, > > 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 > > > >> [[alternative HTML version deleted]] > > > >> ______________________________________________ > >> R-help@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 > > > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@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@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.
