blimit function

Basic Local Independence Model Identification Analysis

Basic Local Independence Model Identification Analysis

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

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.

Returns

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. 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)
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