Week 11: Collinearity (03/23/2023)

Ozlem Tuncel

otuncelgurlek1@gsu.edu

⚠️ CAUTION: DO NOT SOLELY RELY ON MY NOTES. THERE MIGHT BE TYPOS AND MISTAKES. ALWAYS TAKE YOUR NOTES!

✔️ The goal of this week is understanding multicollinearity issue in depth.

You will be doing peer-review this week. So, here is how to hone your peer-review skills:

Around 1.5 page, and nothing less or more is not helpful.
Introduction should be a one paragraph of brief summary of the manuscript, and your overall comment about the contribution.
Main body should be about main criticisms. 3 is the ideal number of major concerns. Spend a paragraph on each. If it is an obvious mistake, do not explain why. But if that is not a obvious one, make sure to include an explanation. Pair your criticism with a suggestion.
End with minor points with bullet points. Major typos, formatting issues, aesthetics … are some of the examples of minor issues.

## Here are some key points from the lecture:

Perfect multicollinearity deals with $X$. We assume that X is full rank, $N>k$, and sufficient variability in $X$.
If our coefficients add up to zero - this is perfect multicollinearity.
Theoretically, this is a major problem. In real life, it is not because R will not produce results for the variable causing this error.
You need more observations than your number of variables. This is problematic theoretically and practically because R will produce NaN.
Colinearity is really easy to diagnose with Pearson’s R. But, multicollinearity is tricky because it can exist even with relatively low pairwise correlation.
Multicollinearity is sample problem.

Achen, C. H. (2002). Toward a new political methodology: Microfoundations and ART. Annual Review of Political Science, 5(1), 423-450.