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.

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. 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)
#> 1/13 0000 
#> 2/13 0001 
#> 3/13 0010 
#> 4/13 0011 
#> 5/13 0100 
#> 6/13 0101 
#> 7/13 0110 
#> 8/13 0111 
#> 9/13 1000 
#> 10/13 1001 
#> 
#> 
#> B L I M I T
#> BASIC LOCAL INDEPENDENCE MODEL IDENTIFICATION ANALYSIS
#> 
#> Number of items:                  4 
#> Number of knowledge states:       6 
#> 
#> Total number of parameters:       13 
#> Jacobian matrix rank:             10 
#> Null space dimension (NSD):       3 
#> Identification problems detected:
#> Jacobian matrix is not full rank.
#> 
#> Submatrix rank analysis table
#> [BETA] = submatrix of the careless error parameters
#> [ETA]  = submatrix of the lucky guess parameters
#> [PI]   = submatrix of the state probabilities
#>       SUBMATRIX NPAR RANK NSD TRADEOFF_DIM
#> 1        [BETA]    4    4   0            0
#> 2         [ETA]    4    4   0            0
#> 3          [PI]    5    5   0            0
#> 4    [BETA ETA]    8    8   0            0
#> 5     [BETA PI]    9    8   1            1
#> 6      [ETA PI]    9    8   1            1
#> 7 [BETA ETA PI]   13   10   3            1
#> 
#> 
#> Item diagnostics for [BETA PI] submatrix
#> Second-order tradeoff dimensions:    1 
#> -------------------------------
#>   PARAMS  BETA  DIM1
#> 1  BETA1 0.056  0.00
#> 2  BETA2 0.305  0.00
#> 3  BETA3 0.299 -0.62
#> 4  BETA4 0.305  1.00
#> -------------------------------
#> 
#> 
#> Item diagnostics for [ETA PI] submatrix
#> Second-order tradeoff dimensions:    1 
#> -------------------------------
#>   PARAMS   ETA  DIM1
#> 1   ETA1 0.422 -1.02
#> 2   ETA2 0.314  1.00
#> 3   ETA3 0.005  0.00
#> 4   ETA4 0.114  0.00
#> -------------------------------
#> 
#> 
#> Item diagnostics for [BETA ETA PI] submatrix
#> Third-order tradeoff dimensions:    1 
#> -------------------------------
#>   PARAMS VALUES DIM1
#> 1  BETA1  0.056  0.0
#> 2  BETA2  0.305  0.0
#> 3  BETA3  0.299 -1.7
#> 4   ETA1  0.422  1.0
#> 5   ETA3  0.005  0.0
#> 6   ETA4  0.114  0.0
#> -------------------------------