Jacobian Matrix for Basic Local Independence Model

Description

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

Usage

1
2
3
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.

Details

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

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.

References

Heller, J. (2016). Identifiability in probabilistic knowledge structures. Manuscript under revision.

Stefanutti, L., Heller, J., Anselmi, P., & Robusto, E. (2012). Assessing the local identifiability of probabilistic knowledge structures. Behavior Research Methods, 44, 1197–1211.

See Also

blim, simulate.blim, gradedness.

Examples

1
2
3
4
5
6
7
data(endm)
blim1 <- blim(endm$K2, endm$N.R)

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