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 th subject is omitted, the likelihood displacement is

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

wher is the score residual vector of the th subject. 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 is the matrix with rows that are the score residual vectors . The elements of the eigenvector associated with the largest eigenvalue of the matrix , 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 th subject on the global fit of the model is proportional to the magnitude of , where is the th element of the vector that satisfies

with being the largest eigenvalue of . 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.