blimit – pks

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. doi:10.3758/s13428-012-0187-z

Examples

library("pks")

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
-------------------------------

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