- High leverage points are observations that hae outlying values in covariate space
**Popular (recent) method from Imon(2006) is to use the distance from the mean (DM) diagnostic to identify these points**- It may however suffer from masking and swamping effects, due to low leverage points
- In a logistic regression most of the extreme points in the covariaite pattern may have the smallest leverage values
- Thus detecting high leverage points in logistic regression based on the leverage values method in linear regression is unsuccessful
- Cut off point for any $latex b_j $ DM: $latex b_j \geq Median(b_j) + c.MAD(b_j) $ with $latex MAD(b_j) = Median{|b_j-Median(b_j)|}/0.6745 $ and c a constant to choose as 2 or 3
**Proposing the Robust Logistic Diagnostic (RLGD) mixing the DM technique and the Diagnostic Robust Generalized Potentials from Habshah (2009)**- First stage identifies high leverage points using robust estimator either using Minimum Covariance Determinants (MDC) or Minimum Volume Ellipsoid (MVE) (Rousseeuw 1984) then use the diagnostic approach to confirm
**step 1**: For each ith point compute the RMD using either MCD or MVE estimators**step 2**: Ith points with $latex RMD_i>Median(RMD_i) + c.MAD(RMD_i)$ are suspected as high leverage points and two sets are created, one with without the high leverage values and one with only the leverage values**step 3**: Compute $latex b_i$ for set with high leverage points**step 4**: Delete $latex b_i$ greater than the cut off value

- Performane of the DM method and the RLGD method were compared using the Detection Capacity and the False Alarm rate.
- The RLGD method has a better detection probability and a false alarm rate up to 20%, better than the DM method.

# Robust logistic diagnostic for the identification of high leverage points in logistic regression model

Original by B.A Syaiba, M. Habshah, University Putra Malaysia, 2010, 9 pages## Latest Hamster Notes

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