# Leverage - influential points

Do we look at the absolute value of the leverage or the relative value?

For instance, based on the chart below, the largest leverage is about 0.023, it is big compared to other data points, but I'm not sure if there's something like threshold in VIF that indicating a high leverage? I have seen three rules of thumb that depend on $k$, the number of predictors (including the constant), and on $n$, the number of observations.

The average value of L is $\frac{k}{n}$, and you want to examine observations where the leverage is extreme relative to that value.

The ROTs are:

• L $> \frac{2k}{n}$ indicates high leverage (twice the average)
• For small samples, you may want to use $L>\frac{3k}{n}$ (three times the average)
• Others say a point with leverage greater than $\frac{2k+2}{n}$ should be carefully examined

I am not aware of any rigorous foundations for these, though they may exist.

• Thanks @Dimitriy! If the variables are categorical, do I need to count the level? – sufeipopo Aug 21 '14 at 19:01
• Let's say you have $m$ continuous variables and one categorical variable with $l$ levels. If you are including the latter as a set of $l-1$ binary indicators to avoid the dummy variable trap, then you would have $k=l + m$, counting the constant as one variable. – Dimitriy V. Masterov Aug 21 '14 at 20:06