Multicollinearity in regression is one of those issues that strikes fear into the hearts of researchers. You’ve heard about its dangers in statistics
classes, and colleagues and journal reviews question your results because of it. But there are really only a few causes of multicollinearity. Let’s explore them.
Multicollinearity is simply redundancy in the information contained in predictor variables. If the redundancy is moderate,
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Multicollinearity is one of those terms in statistics that is often defined in one of two ways:
1. Very mathematical terms that make no sense — I mean, what is a linear combination anyway?
2. Completely oversimplified in order to avoid the mathematical terms — it’s a high correlation, right?
So what is it really? In English?
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Multicollinearity can affect any regression model with more than one predictor. It occurs when two or more predictor variables overlap so much in what they measure that their effects are indistinguishable.
When the model tries to estimate their unique effects, it goes wonky (yes, that’s a technical term).
So for example, you may be interested in understanding the separate effects of altitude and temperature on the growth of a certain species of mountain tree.
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There is a bit of art and experience to model building. You need to build a model to answer your research question but how do you build a statistical model when there are no instructions in the box?
Should you start with all your predictors or look at each one separately? Do you always take out non-significant variables and do you always leave in significant ones?
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I recently gave a free webinar on Principal Component Analysis. We had almost 300 researchers attend and didn’t get through all the questions. This is part of a series of answers to those questions.
If you missed it, you can get the webinar recording here.
Question: Can we use PCA for reducing both predictors and response variables?
In fact, there were a few related but separate questions about using and interpreting the resulting component scores, so I’ll answer them together here.
How could you use the component scores?
A lot of times PCAs are used for further analysis — say, regression. How can we interpret the results of regression?
Let’s say I would like to interpret my regression results in terms of original data, but they are hiding under PCAs. What is the best interpretation that we can do in this case?
Answer:
So yes, the point of PCA is to reduce variables — create an index score variable that is an optimally weighted combination of a group of correlated variables.
And yes, you can use this index variable as either a predictor or response variable.
It is often used as a solution for multicollinearity among predictor variables in a regression model. Rather than include multiple correlated predictors, none of which is significant, if you can combine them using PCA, then use that.
It’s also used as a solution to avoid inflated familywise Type I error caused by running the same analysis on multiple correlated outcome variables. Combine the correlated outcomes using PCA, then use that as the single outcome variable. (This is, incidentally, what MANOVA does).
In both cases, you can no longer interpret the individual variables.
You may want to, but you can’t. (more…)
Multicollinearity isn’t an assumption of regression models; it’s a data issue.
And while it can be seriously problematic, more often it’s just a nuisance.
In this webinar, we’ll discuss:
- What multicollinearity is and isn’t
- What it does to your model and estimates
- How to detect it
- What to do about it, depending on how serious it is
Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.
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