# vcov.mpt

##### Covariance and Information Matrix for MPT Models

Returns the covariance matrix or the Fisher information matrix of a fitted
`mpt`

model object.

- Keywords
- models

##### Usage

```
# S3 method for mpt
vcov(object, logit = FALSE, what = c("vcov", "fisher"), …)
```

##### Arguments

- object
an object of class

`mpt`

, typically the result of a call to`mpt`

.- logit
logical. Switch between logit and probability scale.

- what
character. If

`vcov`

(default), the covariance matrix is returned; if`fisher`

, the Fisher information matrix is returned.- …
further arguments passed to or from other methods. None are used in this method.

##### Details

If `logit`

is false, the covariance matrix is based on the observed
Fisher information matrix of the ML estimator on the probability scale.
This is equivalent to the equations for the covariance matrix given in Hu
and Batchelder (1994) and Hu (1999), although the implementation here is
different.

If `logit`

is true, the covariance matrix and the estimated information
matrix (Elandt-Johnson, 1971) of the ML estimator on the logit scale are
obtained by the multivariate delta method (Bishop, Fienberg, and Holland,
1975; Grizzle, Starmer, and Koch, 1969).

##### Value

A (named) square matrix.

##### References

Bishop, Y.M.M., Fienberg, S.E., & Holland, P.W. (1975).
*Discrete multivariate analysis: Theory and practice*.
Cambridge: MIT Press.

Elandt-Johnson, R. C. (1971).
*Probability models and statistical methods in genetics*.
New York: Wiley.

Grizzle, J.E., Starmer, C.F., & Koch, G. (1969).
Analysis of categorical data by linear models.
*Biometrics*, 25, 489--504.
10.2307/2528901

Hu, X. (1999).
Multinomial processing tree models: An implementation.
*Behavior Research Methods, Instruments, & Computers*, **31**,
689--695.
10.3758/BF03200747

Hu, X., & Batchelder, W.H. (1994).
The statistical analysis of general processing tree models with the EM
algorithm.
*Psychometrika*, **59**, 21--47.
10.1007/bf02294263

##### See Also

`mpt`

.

##### Examples

```
# NOT RUN {
data(retroact)
m <- mpt(mptspec("SR"), retroact[retroact$lists == 1, ])
vcov(m) # covariance matrix (probability scale)
vcov(m, logit = TRUE) # covariance matrix (logit scale)
vcov(m, what = "fisher") # Fisher information
# }
```

*Documentation reproduced from package mpt, version 0.6-2, License: GPL (>= 2)*