vcov.mpt {mpt} | R Documentation |
Covariance and Information Matrix for MPT Models
Description
Returns the covariance matrix or the Fisher information matrix of a fitted
mpt
model object.
Usage
## S3 method for class 'mpt'
vcov(object, logit = FALSE, what = c("vcov", "fisher"), ...)
Arguments
object |
an object of class |
logit |
logical. Switch between logit and probability scale. |
what |
character. If |
... |
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(3), 489–504. doi: 10.2307/2528901
Hu, X. (1999). Multinomial processing tree models: An implementation. Behavior Research Methods, Instruments, & Computers, 31(4), 689–695. doi: 10.3758/BF03200747
Hu, X., & Batchelder, W.H. (1994). The statistical analysis of general processing tree models with the EM algorithm. Psychometrika, 59(1), 21–47. doi: 10.1007/bf02294263
See Also
mpt
.
Examples
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