blimit: Basic Local Independence Model Identification Analysis

In pks: Probabilistic Knowledge Structures

Basic Local Independence Model Identification Analysis

Description

Tests the local identifiability of a basic local independence model (BLIM).

Usage

blimit(K, beta = NULL, eta = NULL, pi = NULL, file_name = NULL)

Arguments

K	a state-by-problem indicator matrix representing the knowledge structure. An element is one if the problem is contained in the state, and else zero.
beta, eta, pi	vectors of parameter values for probabilities of careless errors, lucky guesses, and knowledge states, respectively.
file_name	name of an output file.

Details

See Stefanutti et al. (2012) for details.

The blimit function has been adapted from code provided by Andrea Brancaccio, Debora de Chiusole, and Luca Stefanutti. It contains a function to compute the reduced row echelon form based on an implementation in the pracma package.

Value

A list having the following components:

NItems	the number of items.
NStates	the number of knowledge states.
NPar	the number of parameters.
Rank	the rank of the Jacobian matrix.
NSD	the null space dimension.
RankBeta, RankEta, RankPi, RankBetaEta, RankBetaPi, RankEtaPi	the rank of submatrices of the Jacobian.
DiagBetaEta, DiagBetaPi, DiagEtaPi, DiagBetaEtaPi	diagnostic information about specific parameter trade-offs.
Jacobian	the Jacobian matrix.
beta, eta, pi	the parameter values used in the analysis.

References

Stefanutti, L., Heller, J., Anselmi, P., & Robusto, E. (2012). Assessing the local identifiability of probabilistic knowledge structures. Behavior Research Methods, 44(4), 1197–1211. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3758/s13428-012-0187-z")}

See Also

blim, jacobian.

Examples

K <- as.binmat(c("0000", "1000", "0100", "1110", "1101", "1111"))

set.seed(1234)
info <- blimit(K)

pks documentation built on July 9, 2023, 5:43 p.m.