🚀 go-pugleaf

Pregibon's logistic regression diagnostics (1981,Annals of Stats,p705)
for outliers and leverage points are based on the IRLS algorithm for
fitting logistic regression. What he does is to consider a single WLS
step using the converged values of the weights and working dependent
variable. Essentially this means he approximates the mle estimate, a
nonlinear functional of the data, by a linear functional of the data
locally in the neighbourhood of the observed data.

I don't see why the approach could not be applied to collinearity
diagnostics as well, thus the major modification to the standard
linear model treatment would be to incorporate the weights from the
IRLS procedure.

This approach might not be as successful for other link functions
than the logistic, eg probit regression, because the logistic link
function is canonical for the binomial or Bernoulli distribution and
the one-step approximation is not as good when a non-canonical link
is used.

Murray Jorgensen
Department of Mathematics and Statistics
University of Waikato, Hamilton, New Zealand