genQ {cdmTools}

Generate Q-matrix

Description

Generates a Q-matrix. The criteria from Chen, Liu, Xu, & Ying (2015) and Xu & Shang (2018) can be used to generate identifiable Q-matrices. Only binary Q-matrix are supported so far. Useful for simulation studies.

Usage

genQ(J, K, Kj, I = 2, min.JK = 3, max.Kcor = 1, Qid = "none", seed = NULL)

Arguments

J

Number of items.

K

Number of attributes.

Kj

A vector specifying the number (or proportion, if summing up to 1) of items measuring 1, 2, 3, ..., attributes. The first element of the vector determines the number (or proportion) of items measuring 1 attribute, and so on. See Examples.

I

Number of identity matrices to include in the Q-matrix (up to column permutation). The default is 2.

min.JK

Minimum number of items measuring each attribute. It can be overwritten by I, if I is higher than min.JK. The default is 3.

max.Kcor

Maximum allowed tetrachoric correlation among the columns to avoid overlapping (Nájera, Sorrel, de la Torre, & Abad, 2020). The default is 1.

Qid

Assure that the generated Q-matrix is generically identifiable. It includes "none" (for no identifiability assurance), "DINA", "DINO", or "others" (for other CDMs identifiability). The default is "none".

seed

A seed for obtaining consistent results. If NULL, no seed is used. The default is NULL.

Value

genQ returns an object of class genQ.

gen.Q

The generated Q-matrix (matrix).

JK

Number of items measuring each attribute (vector).

Kcor

Tetrachoric correlations among the columns (matrix).

is.Qid

Q-matrix identifiability information (list).

specifications

Function call specifications (list).

Author(s)

Pablo Nájera, Universidad Pontificia Comillas

References

Chen, Y., Liu, J., Xu, G., & Ying, Z. (2015). Statistical analysis of Q-matrix based diagnostic classification models. Journal of the American Statistical Association, 110, 850-866. https://doi.org/10.1080/01621459.2014.934827

Nájera, P., Sorrel, M. A., de la Torre, J., & Abad, F. J. (2020). Balancing fit and parsimony to improve Q-matrix validation. British Journal of Mathematical and Statistical Psychology. https://doi.org/10.1111/bmsp.12228

Xu, G., & Shang, Z. (2018). Identifying latent structures in restricted latent class models. Journal of the American Statistical Association, 113, 1284-1295. https://doi.org/10.1080/01621459.2017.1340889

Examples

Kj <- c(15, 10, 0, 5) # 15 one-att, 10 2-atts, 0 3-atts, and 5 four-atts items
Q <- genQ(J = 30, K = 4, Kj = Kj, Qid = "others", seed = 123)