Generate a Random Q-matrix

generate a \(I\) × \(K\) Q-matrix randomly, which consisted of one-attribute q-vectors (50 This function ensures that the generated Q-matrix contains at least two identity matrices as a priority. Therefore, this function must also satisfy the condition that the number of items (\(I\)) must be at least twice the number of attributes (\(K\)).

sim.Q(K, I, att.str = NULL)

Arguments

K

The number of attributes of the Q-matrix.

I

The number of items.

att.str

Specify attribute structures. NULL, by default, means there is no structure. Attribute structure needs be specified as a list - which will be internally handled by att.structure function. See examples. It can also be a matrix giving all permissible attribute profiles.

Value

An object of class matrix.

References

Najera, P., Sorrel, M. A., de la Torre, J., & Abad, F. J. (2021). Balancing fit and parsimony to improve Q-matrix validation. Br J Math Stat Psychol, 74 Suppl 1, 110-130. DOI: 10.1111/bmsp.12228.

Author

Haijiang Qin <Haijiang133@outlook.com>

Examples

library(Qval)

set.seed(123)

Q <- sim.Q(5, 10)
print(Q)
#>         A1 A2 A3 A4 A5
#> item 1   0  0  1  0  0
#> item 2   0  0  0  0  1
#> item 3   0  1  0  0  0
#> item 4   0  0  1  0  0
#> item 5   1  0  0  0  0
#> item 6   0  0  0  1  0
#> item 7   1  0  0  0  0
#> item 8   0  1  0  0  0
#> item 9   0  0  0  0  1
#> item 10  0  0  0  1  0