pks (version 0.4-1)

jacobian: Jacobian Matrix for Basic Local Independence Model

Description

Computes the Jacobian matrix for a basic local independence model (BLIM).

Usage

jacobian(object, P.K = rep(1/nstates, nstates),
         beta = rep(0.1, nitems), eta = rep(0.1, nitems),
         errtype = c("both", "error", "guessing"))

Arguments

object

an object of class blim, typically the result of a call to blim.

P.K

the vector of parameter values for probabilities of knowledge states.

beta

the vector of parameter values for probabilities of a careless error.

eta

the vector of parameter values for probabilities of a lucky guess.

errtype

type of response errors that can occur: error for careless errors only, guessing for lucky guesses only, and both for both error types.

Value

The Jacobian matrix. The number of rows equals 2^(number of items) - 1, the number of columns equals the number of independent parameters in the model.

Details

This is a draft version. It may change in future releases.

References

Heller, J. (2017). Identifiability in probabilistic knowledge structures. Journal of Mathematical Psychology, 77, 46--57. 10.1016/j.jmp.2016.07.008

Stefanutti, L., Heller, J., Anselmi, P., & Robusto, E. (2012). Assessing the local identifiability of probabilistic knowledge structures. Behavior Research Methods, 44, 1197--1211. 10.3758/s13428-012-0187-z

See Also

blim, simulate.blim, gradedness.

Examples

# NOT RUN {
data(endm)
blim1 <- blim(endm$K2, endm$N.R)

## Test of identifiability
J <- jacobian(blim1)
dim(J)
qr(J)$rank
# }