Score residuals for detecting outlying subjects.

## Arguments

- x
A fitted multi-state model, as returned by

`msm`

.- plot
If

`TRUE`

, display a simple plot of the residuals in subject order, labelled by subject identifiers

## 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 \(I(\theta)\) 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).

## Author

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