## Influence of Observations on Overall Fit of the Model

The LD statistic
approximates the likelihood displacement, which
is the amount by which minus twice the
log likelihood (), under a fitted model,
changes when each subject in turn is left out. When the *i*th
subject is omitted, the likelihood displacement is

where is the vector of parameter estimates obtained by
fitting the model without the *i*th subject.
Instead of refitting the model without the *i*th subject,
Pettitt and Bin Daud (1989) propose that the likelihood
displacement for the *i*th subject be approximated by

This approximation is output to the LD= variable.

The LMAX statistic
is another global influence statistic. This statistic
is based on the symmetric matrix

where **L** is the matrix with rows that are the score
residual vectors **L**_{i}.
The elements of the eigenvector associated with the
largest eigenvalue of the matrix **B**, standardized to unit length,
give a measure of the sensitivity
of the fit of the model to each observation in the data. The influence
of the *i*th subject on the global fit of the model is proportional
to the magnitude of , where is the *i*th element
of the vector that satisfies

with being the largest eigenvalue of **B**.
The sign of is irrelevant, and its absolute
value is output to
the LMAX= variable.
When the counting process MODEL specification is
used, the LD= and LMAX= variables are set to missing, because these two
global influence statistics can be calculated on a per subject
basis only.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.