Hat Matrix Leverage Points

The hat matrix is often used as diagnostics to identify leverage points 10.

Hat matrix leverage points. The average leverage is therefore p1 n T 20 November 2015. Each point of the data set tries to pull the ordinary least squares OLS line towards itself. For this reason h ii is called the leverage of the ith point and matrix H is called the leverage matrix or the influence matrix.

However the value for the diagonal element of the hat matrix HI is very large. The hat matrix is calculated as. H X X T X 1 X T.

Haty H y The diagonal elements of this matrix. This point does not affect the estimates of the regression coefficients. This is a leverage point.

1 12 w x X X x i n 5 i T T ii i. Rousseeuw and Zomeren 22 p 635 note that leverage is the name of the effect and that the diagonal elements of the hat matrix h ii as well as the Mahalanobis distance see later or similar robust measures are diagnostics that try to quantify this effect. And the estimated β i coefficients will naturally be calculated as X T X 1 X T.

Usually we treat the n values hi as a batch of numbers and. The hat matrix provides a measure of leverage. Outlying Xobservation and hat matrixleverage values In uential cases.

The average size of a diagonal element of the hat matrix then is pn. Leverage considered large if it is bigger than. Looking at the covariates alone.