Robust Regression Examples |
This section is based entirely on
Rousseeuw and Van Zomeren (1990).
Observations , which are far away from most of
the other observations, are called leverage points.
One classical method inspects the Mahalanobis
distances
to find outliers
:
Note that the MVE subroutine prints the classical Mahalanobis
distances together with the robust distances
.
In classical linear regression, the diagonal
elements
of the hat matrix
The definition of a leverage point is, therefore,
based entirely on the outlyingness of
and is not related to the response value
.
By including the
value in the definition,
Rousseeuw and Van Zomeren (1990) distinguish between
the following:
Rousseeuw and Van Zomeren (1990) propose to plot the
standardized residuals of robust regression (LMS or LTS)
versus the robust distances obtained from MVE.
Two horizontal lines corresponding to residual
values of
and -2.5 are useful to distinguish
between small and large residuals, and one vertical
line corresponding to the
is
used to distinguish between small and large distances.
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