Description

Score residuals for detecting outlying subjects.

Usage

Arguments

Details

The score residual for a single subject is

U(theta)^T I(theta)^{-1} U(theta)

where U(theta) is the vector of first derivatives of the log-likelihood for that subject at maximum likelihood estimates theta, and theta is the observed Fisher information matrix, that is, the matrix of second derivatives of minus the log-likelihood for that subject at theta.

Subjects with a higher influence on the maximum likelihood estimates will have higher score residuals.

These are only available for models with analytic derivatives (which includes all non-hidden and most hidden Markov models).

Value

Vector of the residuals, named by subject identifiers.

Author(s)

Andrew Titman a.titman@lancaster.ac.uk (theory), Chris Jackson chris.jackson@mrc-bsu.cam.ac.uk (code)