1. Model Diagnostics
Political Analysis II

2. Why should we care about unusual observations?
Because they can drive our results and lead to misleading findings (especially in small samples)
To improve our theory and statistical model
Three types of unusual observations:
Regression outliers
High leverage observations
Influential observations

3. A useful tool: Residuals

4. Regression outliers
Regression outliers have extreme values for Y given their values on X
For example, oil-rich non-democracies
Why? Coding error, peculiarity
Effect: limited, but they can increase our standard errors
Detect: large studentized residuals (> |2|)
Fix: Check coding, revise theory
Fox (2008)

5. Example of regression outliers (1)
Remember that Lijphart excluded India and Israel from his analysis because they had extreme values on the dependent variable of political stability and absence of violence? (i.e. univariate outliers)

6. Example of regression outliers (2)
Remember that Lijphart excluded India and Israel from his analysis because they had extreme values on the dependent variable of political stability and absence of violence? (i.e. univariate outliers)
Only Israel, however, is a regression outlier!

7. High leverage observations
High leverage observations have extreme values on one or more independent variables.
Effect: They can change the estimate of regression coefficients (if they don’t follow the pattern of the data)
Detect: hat values (measure based on the fitted/Y-hat values)
Fox (2008)

8. Example of high leverage observations
Lijphart described India as an “extreme outlier”, but it is actually a high leverage observation.

9. Example of high leverage observations
Lijphart described India as an “extreme outlier”, but it is actually a high leverage observation.

10. Example of high leverage observations
We can see this clearly when we look at India’s very high hat-values.

11. Influential observations
Influential observations have extreme values for X and Y
Influence = Outlierness X Leverage
Effect: removing them from the model significantly changes the direction, strength, or significance of the results
Detect: studentized residuals versus leverage, Cook’s Distance
Fix: check coding, “dummying out”, re-run the model without the observation(s) and compare results
Fox (2008)

12. Example of influential observations
No influential observations in Lijphart’s sample…
India: high hat-values, but small residuals
Israel: large residuals, but low hat-values
We find influential observations in the lower-right corner and upper-right corner (not shown here).

13. The infamous butterfly ballot
Wand et al. (2001) show that more than 2,000 Democrats voted for Buchanan in Palm Beach County, a typically Democratic county, due to the butterfly ballot. This type of ballot was only used in this county and only for election-day for president.
As a result, George W. Bush, and not Al Gore, won Florida and the presidency.
Kellstedt and Whitten (2013)

15. What should we do with unusual observations?
Don’t ignore it
Learn to understand why an observation is unusual
If it is a coding error, recode it; if that’s not possible, drop it
Learn more about the observation and improve your model
Transform the data (e.g. log transformation)
More on nonlinear relationships next week

16. Multicollinearity
Multicollinearity is the high correlation between two or more independent variables.
For example, height and weight
Ideology and party ID
Effect: larger standard errors ( Type II errors), unstable coefficients
Detect: variance-inflation factor VIF (VIF > 10 are problematic)
Fix: not easy, but increasing sample size, centering variables, or combining variables into an index can help.
Kellstedt and Whitten (2013: 238)

17. More articles on influential observations
Fails and Krieckhaus (2010). Colonialism, Property Rights and the Modern World Income Distribution. British Journal of Political Science, 40(3), Data: property-rights-and-the-modern-world-income-distribution
Wand et al. (2001). The Butterfly Did It: The Aberrant Vote for Buchanan in Palm Beach County, Florida. American Political Science Review, 95(4), Data: