Posted by
Poes, Matthew Joseph on
Aug 08, 2012; 2:19pm
URL: http://spssx-discussion.165.s1.nabble.com/Multicolinearity-tp5714614p5714630.html
Thanks Stephen,
I also cited a few articles in a response to Rich's email, as he apparently doesn't by the evidence.
I should note that I made a comment that you can't get "valid" results using OLS regression because the multicolinearity exists and can't be eliminated. This is overstating things, and the real argument is that the coefficients themselves should be unbiased even in light of the multicolinearity, give you valid coefficients, but possibly have some stability issues in the model. I've heard a lot of arguments on this, obviously read a lot of papers on the topic, and over the last 5 years, I myself have been involved in numerous roundtable discussions trying to develop a best practice recommendation for the testing of interactions (moderation). These best practices are intended to go into white papers that would go along with certain federal grants, basically stating that results will only be considered valid if they follow certain procedures or meet certain criteria. Moderation is one that has simply not been easy to nail down. There are some very knowledgeable fol!
ks who are arguing very adamantly that OLS is completely inappropriate, and have suggested models utilizing SEM, varying parameter models, and even some suggestions of developing models using instrumental variables in an SEM structure (this was an off the cuff comment, I believe it to actually be incorrect, FYI).
So while I'm sure all this is confusing to the young stat students out there, let me just say: Moderation effects (Interactions) are going to be a commonly tested phenomena in social sciences. It's very likely that you will be taught two things that are incorrect in your stats courses, and this may even happen at graduate level courses (it did for me). The first is that mean centering solves the problem created by multicolinearity, it does not. The second is that it makes for easy interpretation of main effects, and while centering does make it easier to interpret main effects, the model that contains the interaction coefficient does not have main effects, it has conditional effects. You will likely be taught to use a 2-step regression, the first step of that regression will contain the main effects, and the second step will add the interaction term, and in this step, the two "main effects" turn into conditional effects, as they are now conditional on the value !
of the interaction effect. The next thing I think you need to know is that most everyone has probably interpreted an interaction model incorrectly at least once in their life (myself included). Try to remember what I've said here, review the literature, tons of recent literature exists on interpreting interactions correctly, and carefully consider the interaction you are trying to interpret, and what it likely means. The final thing I'll say is that plotting is your friend. It takes a while to wrap your head around the interpretation of conditional effects like interactions, and as such, I find that plots make it much easier. In fact, I consider any paper written that contains an interaction and hasn't plotted it to be unacceptable, unless it's in a statistics journal, as I don't consider the average audience of these journals capable of easily interpreting the effects.
One last story, in case it helps: In my last PhD stats course I had a professor who lightly covered this topic. His knowledge of the core topic at hand, MLM/HLM was great, but his knowledge of interactions was dated. While I accepted what I was taught in earlier years, by this point I had read enough articles and run enough models to know this wasn't true. We were learning about lower level moderation in multi-level models. I argued with the professor that while all of the lesson made sense as a whole, his insistence that he would mark our homework and test questions wrong if we didn't mean center for the interaction was in error. In fact I said that mean centering for MLM was, at his own admission, solely for interpretation purposes, and that if someone didn't do it, but correctly interpreted the effects, they should not be marked off, as this would simply reflect a deeper understanding than most. I presented him with all the evidence, and his final statement!
to me was that his course was approved by the department, this was the departments accepted view, and while he agreed the literature appears to suggest their view is wrong, he will still hold us all to it. Obviously I went along, centered as he requested in both the single level and multilevel models. However, the following year, when the course was offered again, the department had met and decided recent (a relative term since some of this dates back to the 80's)has shown the hard stance they took was wrong. The course was changed, our departments graduate stats courses were changed, and four separate dissertations were given a revise and resubmit due to explicit claims of fixing multicolinearity. I think this story is important because its telling as to how engrained these ideas are.
Matthew J Poes
Research Data Specialist
Center for Prevention Research and Development
University of Illinois
510 Devonshire Dr.
Champaign, IL 61820
Phone: 217-265-4576
email:
[hidden email]
-----Original Message-----
From: StatisticsDoc [mailto:
[hidden email]]
Sent: Tuesday, August 07, 2012 7:39 PM
To: Poes, Matthew Joseph;
[hidden email]
Subject: RE: Multicolinearity.
Matthew,
Good point about mean centering. Stats students are exposed to so much "received wisdom" about the supposed benefits of mean centering that it might be helpful to mention a couple of papers that will set the inquiring student in the right direction:
Echambi & Hess (2007). Mean-Centering Does Not Alleviate Collinearity Problems in Moderated Multiple Regression Models. Marketing Science, 26(3), 438-445.
Shieh (2011). Clarifying the role of mean centring in multicollinearity of interaction effects. British Journal of Mathematical and Statistical Psychology, 64(3), 462-477.
Dalal & Zickar (2011). Some Common Myths About Centering Predictor Variables in Moderated Multiple Regression and Polynomial Regression.
Organizational Research Methods, 15(3), 339-362.
These papers note that while mean centering may be desirable for other reasons (interpretability of coefficients), this procedure does not reduce multicollinearity or otherwise improve the accuracy or sensitivity of the parameter estimates.
Best,
Stephen Brand
www.StatisticsDoc.com
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of Poes, Matthew Joseph
Sent: Tuesday, August 07, 2012 5:08 PM
To:
[hidden email]
Subject: Re: Multicolinearity.
Certain authors like Baron and Kenny would argue this resulted because you did your interaction (moderation) analysis incorrectly. They would correctly argue that the same information contained in the interaction term is also contained in the two IV's themselves, and as such are correlated (first explicated in publication by Cohen as I understand it). This correlation will cause a multi-colinearity problem, and the model coefficients would be inaccurate. They would go on to say that by mean centering the IV's the correlation is reduced to the product term of the IV's (the interaction term) and as such you have reduced multicolinearity.
More recent research has shown this not to be true, and so with normal OLS regression, your unfortunately stuck in a situation where you can't do what your trying to do and get valid results (which isn't to say that 100's if not 1000's of people don't still do this).
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